You should watch the Dormammu combo "bible" to get a hang of his game play.
He is best played as your 2nd or last character because he likes to have hyper meter on deck. He is one of those characters who can just throw out random hypers and it would still serve you good because of their speed and/or chip damage. Dormammu + LVL3 XFC + Hyper meter = One of the best anchors in the game because he can kill character with just chip damage alone. But he also likes having assists on deck so having him 2nd is probably your best option.
His combos aren't hard to do and the hit box on his normals are insane.
As far as his teammates go, he can gel with a lot of characters but likes to be with characters who aren't meter hogs themselves. Sentinel is a good combo with Dormammu, I personally like the Purification assist with Sentinel to cover his ass from the air (as an OTG move it sucks, launches enemies to high). You could probably try to cover your approach from the air with Sentinel when he's in flight mode using the Purification assist.
Doom Hidden missile assist is godly with Dormammu but again Doom is high execution character and using him just for his assist ends up being a liability.
I would recommend you try out Deadpool, Wesker or Storm. Storm is a character who has no usage of Shoryuken movements and you don't really need to be high execution with her if you have a handle on her dashes. Wesker is the same because you can just replace his teleports by using the Gun or Fist strike moves into L/M/H for insta-teleporting. Deadpool is a zoner like Dormammu and Dormammu Black Hole can set up hit confirms for Deadpool. All these characters benefit greatly from Sentinel's Drones assist (then again, how doesn't?).
If I were you, I would seriously consider checking out Storm/Dormammu/Sentinel. Simple ground combo, simple air combo, OTG super with Storm's Whirlwind Ice hyper DHC into Sentinel's HSF hyper will do very solid damage due to DHC glitch. You can also more than likely hit confirm Sentinel's Mouth Beam into Dormammu's Chaotic Flame (like say you know will hit someone from full screen with the Beam, just use Beam xx HSF xx Chaotic Flame. Before the first HSF drones hit the guy, you will have cancelled to Dormammy's faster Chaotic Flame hyper which will hit off of the mouth beam and the Drones will add the extra damage).
Even if you decide to swap Storm for Dormammu, Storm's Whirlwind assist comes out fast and you can hit confirm into Finger -> Dark Hole -> Chaotic Flame. Storm also has massive chip game. All of Dorm's hyper easily DHC into Storm's Ice Storm.
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