I love Purphoros, God of the Forge but I think he really doesn't fit within the deck. I mean chances are you wont get devotion, since you want the game to end fairly quickly. Also you don't have many creatures. I'd rather run a couple Chandra's Phoenix instead, but thats just me.

Purphoros, God of the Forge Is coming out, he is just temporary until i find a missing Spellheart Chimera

some Young Pyromancer could be very help full with triggering Purphoros, God of the Forge

Have you looked at Jace, Memory Adept for his zero ability? Would combo really well with Spellheart Chimera . His +1 is good for draw, and his ult is a threat too!

I would take out 1x [turn / burn] for 1x [steam augury]. I feel like the added draw and/or buff to [spellheart chimera] is just worth running 2 of. For similar reasons it may be worth taking out some combination of 2 [shock], [magma jet], and/or [lightning strike] for the added utility of 2 more [izzet charm]'s.

Also maybe build a sideboard? [Counterflux] is great against control decks. 2x more [anger of the gods] for aggro. Throw in that other [turn / burn] I suggested taking out for things that are tough to kill. A few [mizzium mortars] for a cheaper way to take out problem creatures, too.

Just some suggestions from someone else who wants Izzet to be a thing in competitive :)

Do you have all of these cards because I have most of it and I can trade with you for some

Chandra's Phoenix works really well with a lot of burn. Mizzium Mortars over or along with Cyclonic Rift . Keranos, God of Storms when he comes out. Burn your opponent every turn and card drawing.

I'm not sure how competitive your local area is but Lightning Bolt is the red must have and it's only 1.50 on average per bolt. For draw spells try Think Twice because it's instant and has flash back. Izzet Charm is a solid game 1 spell as it does a little bit of everything you could want. Mana Leak is a very cheap spell at 1 dollar a peice and will for a long time counter their stuff. Peek is another card to consider for the budget version of Gitaxian Probe Probe $3 a peice while peek $0.25. Id also suggest Kiln Fiend as another option. Some decks also run Rift Bolt because it's a delayed Lightning Bolt and is cheap.

I think you'd be better served swapping out your current Chandra for a different one.

Chandra, the Firebrand would still allow you to ping target creature or player for 1 instead of both target player and a creature they control. While you lose the element of being able to keep that creature from blocking, it looks like most of your swinging is done by Spellheart Chimera who can grow big and is both flying and trample. The main reason I advocate this card though is her -2, which will give your burn spells more mileage by copying them.

Chandra Ablaze may also be a good choice. The CMC 6 makes it a little pricey, but as you're only packing a 1-of, shouldn't be too big a deal. Her +1 lets you ditch cards like Shock to trade up 2 damage for 4 damage; and then her -7 lets you cast them from the graveyard for that final coffin nail.