I have flame angels in 4 or 5 reef tanks plus one in my daughters classroom tank all are doing fine with the corals. some of them I've had for years. Although several years ago I did have a flame in a reef tank doing fine with the corals until the large Koran angel started nipping at a damaged large polup stony coral shortly there after if I didn't keep the tank heavily fed, every time I'd sit infront of the tank the flame would come look at me, hover above a fleshy coral then dive straight down and take a big nip out of it, then I would get up and feed the tank and everything was fine, the angels had me well trained.
On a sad note both that flame and the Koran angel were cooked in a coral and fish soup when my air conditioner took a lightning strike in July while we were in Alaska at my brothers wedding, The lightning didn't knock out the halides, house was 92 at 2AM and tank probably hit over 100 degrees.