The idea is to use Invoke Calamity with Rituals to cheat our way up to the mana required to cast Dragonstorm, with some spells to trigger Storm along the way. As our dragons are legendary, we only need a storm count of 4 to fetch all of them of them.
Because of how Irencrag Feat works, we need to be careful of how we stack our cards.
So, once you have 5 mana, which you can use Pyretic/Desperate Ritual to ramp up to, cast Invoke Calamity.
Our two cards we need to choose off Invoke Calamity are any one of either Desperate or Pyretic Ritual, and Irencrag Feat.
Off Invoke Calamity's ability, we cast Irencrag Feat first, then cast the Ritual second, putting it on top of Irencrag Feat on the stack.
As the Stack resolves, Ritual will resolve before Irencrag Feat, giving you 1 more spell to cast for the turn, and to spend the 10 red mana you just made. Our final spell is going to be Dragonstorm.
As we cast at least 3 spells before Dragonstorm (Invoke, Ritual, and Irencrag), we get to fetch at least 4 dragons.
Here's the order we need to fetch the Dragon's in, and their roles in this deck:
1st Dragon is always Dragonlord Dromoka. Dromoka prevents the opponent from casting spells in our turn, which switches off any removal they may have been holding up.
2nd and 3rd are Dragonlord Kolaghan and Atarka, World Render. Kolaghan is to give the team haste, so we can win on the turn we combo. Atarka gives the team double strike, which should put us up to enough damage to kill most opponents on the spot.
Drakuseth, Maw of Flames pulls double duty here. On the Strom turn, he's often the 4th dragon and is meant to shoot down any possible flying blockers. His other role is that he's an easy cast off Irencrag Feat, in case we can't combo storm for some reason.
As Invoke Calamity can select cards from both your hand and your graveyard, looting spells have been included to try assemble the combo.
Cathartic Reunion diggs deeper, but also cost more cards to discard.
Cathartic Pyre functions as both early removal and optional looting.
Manamorphose is mostly just a free spell to draw a card and up the storm count. But it can also help with mana fixing if you ever need to cast a dragon.