Niice. Rather stronger than Deep Analysis (how often will you cast your card-draw spells after something else?), but requiring three colours helps make up for that.

Reminds me of Evermind, now I come to think of it. Or Eyes of the Watcher. All your spells gain "If you paid the kicker cost, draw a card".

Or of course Recycle / Null Profusion, which don't charge anything for the kicker, but those have the 6 mana setup cost and a hefty drawback too.

More comprehensively, read it as "All spells you cast have Multikicker and 'For each time this was kicked, draw a card and add 1 to the storm count.'"

Flashback is a complete bombo on it, not that it's likely to ever wind up in the graveyard.

Yeah, that was my thought, too. Most players will assume Promise the Future will go back to your hand after using the Flashback, but it will get exiled all the same. How about ": Return ~ to its owner's hand." Plenty of precedent for that ability.

It's supposed to be a very VERY powerful spell that's not overpowerly broken, and serves as a card engine for control decks

note that if this is countered or exiled, you don't get to ever play it again