This is my version of a budget Legacy Phoenix list. The main changes I made were to add four Lotus Petals and four Manamorphose I think. I cannot find the original list but it was featured on mtgtop8.com about 2 years ago (I can't remember the exact time either: 1~3 years). I have had this deck in a shelf along time, because I finished getting the physical cards somewhere during CoVid. It was probably in 2021, could have also been early 2022 though or late 2020. I am not sure what exact changes I have been doing with the list I have found, but it absolutely didn't play Lotus Petal, which was a weird choice in my opinion, but by then I guess Lotus petal wasn't a budget option anymore (cost around 5€ when Mystery Boosters released for the first time).
The deck itself is a rather unique combination of Burn and Reanimator, since the best opener for the deck will allways be to setup one to four Arclight Phoenix's. Now obviously getting 3 or 4 Phoenix's on the board by triggering is very unlikely, but there are god hands in this deck and they can happen, it's just very high-rolly since you need to draw multiple Phoenix's in combination with Faithless Looting.
1 or 2 Phoenix's are really easy to setup on the other hand. Either you get a combination of Lava Dart, Entomb and a Lotus Petal, plus a land and your still able to deal 5 damage on turn 1, which is HUUGE for turn 1 in accordance with an archetype like Sligh, Burn or RDW, that frequently deals 2 damage on turn 1 going up to 7 (on average) on turn 2. In RB Phoenix you will have dealt 8 damage on turn 2 with a four card starting hand. I say this because Burn decks and the likes usually do not play Lotus Petal or Simian Spirit Guide (I could be wrong on this ~ but I feel like most RDW decks prefer straight up fire-power over additional explosiveness, that doesn't immidiately or virtually kill your opponent). Keep in mind that you will turn a 7 card hand into a 3 card hand pretty quickly. Playing four cards on the play turn 1 is the goal of this deck in particular, which is why I added the Lotus Petal. I do not however recommend or condone playing Simian Spirit Guide in this slot. Firstly because it is a 3 mana dork that you will never play if you can deal upwards of 6 damage for the same mana investment and secondly it just doesn't produce black. Entomb being the MVP in this deck simply because it can get you anything. Phoenix, Looting, Dart or just another Entomb is good enough.
Luckily we do not need to win through Phoenix alone. In fact: playing mono red Burn is quite good on the play as well as on the draw. It doesn't lose much, since at this point it is much easier to also setup a Phoenix. You will need to understand how Burn decks function and how they like to keep advantage, Phoenix just pushes in 6 to 8 more damage that leaves you with additional setup. In specific with a lot of Flashback cards and a cheaper Bedlam Reveler. In fact Bedlam Reveler almost allways goes plus 3. The only exception is if you have (a) land(s) that you do not absolutely need right away (in which case you will most likely play it and just happen to have two lands in hand at the time you want to play your Reveler). I say this in particular, because you will need to learn how to play some turns without lands in order to get your Phoenix's out again after losing them. For this you will be shooting people a lot with free Fireblasts and flashbacked Lava Darts, you will also do this to go for game. I suggest watching Rhystic Study's video "Red Deck Wins" on You-Tube, to not only get a basic understanding of RDW, Burn and Sligh but also get an understanding for how these decks want to function and the indredible nuances as well as the flexibility these decks can have (https://www.youtube.com/watch?v=P5oc_9ObMzc).
Now here are the cards that diverge the gameplan of this deck from other variants of RDW and how 3 cards (technically 12, but 3 different cards) make the deck possible in the first place, as well as which one single card ruins your main gameplan completetely and how you do not be afraid of it, because your technically playing burn.
Entomb is the MVP of the deck. Being able to tutor out every good piece of card board in your deck is allready huge. Doing this while simultaneously being setup and part of the actual combo is crazy! I have allready mentioned above which are your prefered targets, out of the sideboard in particular I also have [Cabal Therapy]. You can get it as part of the combo if you need to interrupt your opponent's combo as well. You can sacrifice a previously summoned Phoenix or Swiftspear in order to take away your opponents cards. And of course it also represents 2 spells for a single mana and can be used offensively on the play, you will need two Lotus Petals though. Entomb is a main part of every combo if you have it. Notice that you will only ever cast 3 Instants or Sorcerys unless you seriously need to deal with something or go for game. Generally it is allways best to let your opponent have to deal with you, not the other way around, it makes it easier to allways be able to return Phoenix's if you have them in your Graveyard. If you have Entomb, you allways have a Phoenix in Graveyard as long as there are some left in your deck. If you need to be reactive though you will lose around two turns worth of setup, meaning your basically tempoing yourself alongside your opponent, since you mostly need to either deal damage to draw cards or you are just looting. The reason being you will most likely double spell anyway and if your opponent is about to drop something so terrible that you need to interact with them on their turn, it is most likely not good enough anyway and your better of focusing the player. You will mostly be drawing for turn, unless you draw your own bomb in Bedlam Reveler, which your opponent will then have to handle immidiately. This thing gets to 8 power really really quickly.
Manamorphose is probably the best card I have ever seen in my entire life! Just kidding! But no card screams Storm harder than filtering the mana and the card you just spent. Now your deck is most likely going to live and die by the color combination you choose. And yes, there will be times where double black is needed. Lotus Petal + Mountain + Manamorphose + Entomb + Entomb is technically a 5 card combo, but practically a four card Phoenix setup for 6 damage on the first turn. So get a feeling for all your cards in hand. quite frankly you will need to choose your colors based on what you need. If the only Phoenix you can get of the top of your deck is an Entomb, you should probably call black mana. Other than that red mana is the default. Every card that isn't Entomb can be cast from your deck and sometimes you will get angry for calling red and drawing Entomb. That's just how it goes and you will need to learn from the entire context of the game in order to decide whether or not it was the right call to not choose red. This is tricky because you cannot know what is on the top of your deck.
Lotus Petal is a card that if you have it, you have it. And with it I mostly mean game. Much similar to burn decks it allows your Swiftspear to attack for 2 damage in the first turn. You do not need the cast for anything but Prowess triggers. Which to be fair are 7 in total, but having two Swiftspears or a Swiftspear plus a Revler is often game. Even without Phoenix. Any two Burn spells plus a free Petal while having two Swiftspears (unblocked) are 8 damage at the minimum. That is mostly enough to win on turn 3 or 4 depending on how fast you are.
The Combo: You will need two mana in either red and/or black. Get an [Arclight Phoenix] into the graveyard, either via [Entomb] or [Faithless Looting] (in the later gamesttages you can also use [Bedlam Reveler] to do the same), then check if you have played 3 Instants and/or Sorcerys. Don't forget your beginning of combat trigger and there you go! Really doesn't matter which three spells it is. One is allready checked off by setting up your Phoenix. That is why you need to understand how to play burn. The whole combo is really just getting the Phoenix into the graveyard and then just playing triple spell burn.
Now let's briefly talk graveyard hate. Your biggest hindderance will be [Surgical Extraction]. People will most likely side that in so they can hit Phoenix, BUT they may also side in [Ley-Line of the Void] or [Relic of Progenitus]. Or any other hate piece. Now you do not need your graveyard to win with this deck, but you will need to play very preservative IF you play against Ley-Line specifically. If your opponent has a good enough hand, do not even bother to setup your graveyard. Instead use your Entombs to fetch, well more Entombs. That will still trigger Prowess and as soon as you see that board out the Bedlam Revelers. You will never be able to play them. Leave the Phoenix in because it is still a 4 mana flyer that bolts your opponent. My personal choice is [Plague Engineer] it is not only incredibly usefull against Wheenie Dekcs, but it is also a relativley cheeap creauter that can trade with your opponents biggy like Reveler. Anything else like full blown graveyard wipes don't bother you at all. You just keep casting spells and hitting your opponent.
But then there are [Extirpate], but more importantly it's incredibly accessible younger brother [Surgical Extraction]. If they hit your Phoenix, forget about your lightning chicken. Unless you know they have it in their deck and you are going first you will not beat this card. My plan in the case of forcing Phoenix is Mountain + Monestary Swiftspear + Lotus Petal attack for two, then cast [Cabal Therapy]. If you pla Therapy this early, your opponent will likely cast Surgical Extraction in order to get rid of Lotus Petal. Which still really hurts! BUT, this is where we META them, by playing our own copy of [Surgical Extraction]! Naming their [Surgical Exraction]. You can pull this off anytime you feel like you are not going to win against a particular card, BUT you will need to go first in order to minimize any form of casulties. Surgical Extraction at four copys can tear through your deck to the point where you cannot win any longer. Losing just Phoenix is perfectly fine! Since you are playing burn, you still have more than enough gas. If you lose Fireball, Lava Dart, Phoenix and Lotus Petal. You are done for today. Because you will no longer be able to do massive amounts of damage in short time windows, you will flood on lands like crazy and until you do you will be mana screwed to the high heavens. Respect the Extraction. It will lose you games and your opponent will most likely pay the black mana, if they have it.