From what I've read, heard, and experianced, its part luck and part stock.
Generally its just luck on wheather an angel will nip at the corals or not. So if they leave the corals alone, you are fine. If not, they are actually nipping at the slime, and usually not the flesh, so the main problem is that they cause the coral to close, thus not feed. This also depends on the corals you stock. Since a lot of soft corals do not taste very nice, they will leave them alone. However, LPS and, more often, SPS corals taste better to them, so there is more of a chance they will nip at those. But weather they will really cause problems can depend on the tank size and stock. If they tank is FULL of a lot of corals, the angel may go from coral to coral, and no pick on one specifically enough to cause it to stay closed. Again, you get luck from the fish in that it may only like one specifically.
Basically, I just wasted time saying, it is mainly luck, and trial and error is really the only way to go.
IMO, never had ANY problems with Potter's or Coral Beauty, and Flames are said to be similar to both of those.