I've got a pair of Flame Angels in my 24gal, and they're fine. They don't pic on anything, other than nipping at the rocks. They eay anything I put in there, be it flake, pellet, freezedried brine, or frozen mysis. I feed them every evening though, and sometimes kick in a few drops of Arcti-pods in the morning just to keep them going (active little guys!). They'll also eat seaweed sheets off of a veggie clip.
These are the 3rd and 4th flames I've had, and none of mine have ever been problems with any corals.
I did have one that didn't like a Pom-Pom crab though, as he kept creeping into the Flames sleepy hole at night, scaring him.