Phoenix cards are pretty awesome in that they have the ability to come back after leaving the board, but at the cost of a lot of mana for pretty mediocre stats. Because of this, the creatures by themselves are slow to come out and pretty weak when they enter the battlefield. So everything here covers our main problems while letting the Phoenix play to its strength.
Draw/ discard power:
Arcum’s Astrolabe, Thrill of Possibility, Chandra’s Regulator, and Seasoned Pyromancer are all here for the early game draws and discards. With the exception of Rekindling Phoenix, we either want or don’t mind having our creatures in the graveyard and set up for getting them out earlier (or at least cheaper) than we would by casting them. Arcum’s Astrolabe fixes the colorless mana from some of the lands if needed, and Seasoned Pyromancer hits the board with a possible 2 creatures, making sure we’re not leaving the battlefield empty early on.
EDIT 3/21/2021
Updating the deck to remove Arcum's Astrolabe, and experimenting with other cards.
Searching:
Expedition Map searches out Inventors' Fair, Inventors' Fair gets Crucible of Worlds, and then you can seek out any artifact you need from there, or you can use the life gain to negate the loss from recycling Wooded-Foothills. The searching might not be necessary with all the draw cards, but it definitely helps when you have no other options.
Consistent mana:
Naturally, drawing cards will allow the deck to hit more lands. However, having Wooded Foothills and Crucible of Worlds is great for always having a land to play, and for reducing the odds of drawing more lands when you want to hit the fun stuff. Crucible also gets the added bonus of letting you recycle Inventors’ Fair and Buried Ruins if you’re using their effects.
Phoenix:
I’ve narrowed this down to the 4 Phoenix cards that manage to (mostly) pull their own weight. Kuldotha Phoenix is kind of the star of the show since most of how I had to build this deck was around this card. Easy discard choice since it comes out for 1 less mana through it’s metalcraft and has haste. Flamewake Phoenix is clearly Kuldotha’s little brother, since these two synergize so well with each other. Magma Phoenix is the board wipe when equipped with the Basilisk Collar, and can turn the entire game upside down if you get a good life boost too. Rekindling Phoenix is more or less the black sheep here, really having no synergy with anything outside of Flamewake’s Monsterous, but it’s a great card by itself and fills up the 4 mana slot better than all the other ones.
Artifact Support:
As mentioned earlier, the creatures we’re playing are far too weak on their own. Basilisk Collar fixes that problem easily, and since all of our Phoenix cards come back, we’re not too concerned on having them die in battle. Altar of Dementia is the best sacrifice outlet, hands down. It’s mostly here to kill Magma Phoenix equipped with Basilisk Collar so your opponent can’t bide time to find a solution, but it can work wonders for just sacrificing something that would die anyway and mill your opponent (or yourself.) With all the Phoenix consistently coming back, this card can get an insane amount of usage.
Life Support:
Since the deck isn’t dropping any creatures before 3 mana, it’s very likely you’ll be taking a lot of damage. Inventors’ Fair and Basilisk Collar should be (hopefully) helping you stay in the game long enough to get the ball rolling.
Rising from the ashes:
You may have already noticed, but everything in this deck can be recycled one way or another. Crucible gets back lands, Buried Ruins gets back artifacts, and the Phoenix cards bring themselves back. The only card that stays dead is Seasoned Pyromancer, but he has a decent grave effect so he can still get multiple uses just like anything else here. As long as a card isn't exiled, you have the potential to play it again.
I wanted to build a deck that fit the Phoenix theme of Immortality and overall I feel this is a solid build. It may require a few tweaks to fit your taste, but at the very least this can serve as a blueprint in case you were interested in building a modern Phoenix Tribal deck. Feel free to let me know your thoughts on the deck and what changes you would make. I realize this may not be fast enough to be competitive in the Modern format, but it’s a fun deck and definitely powerful if you’re playing with 3 or more players.