I am no expert and have little experience.. but everything I've read and heard says that the Flame and Coral Beauty (and others) are cautionary with reefs - its sort of a matter of luck. My flame angel didn't live long enough to know. I keep my coral beauty in my FOWLR tank.
That is just a risk you have to take. Keep in mind some are safer than others, like the coral beauty but many just are riskier like the lemonpeel angel. I had a flame in my reef and a coral beauty and they were fine, they nipped on the rare occasion but never did any real harm.