Flameback- It really depends on your fish stock and what any angel see as a threat. Fish size, tank size, being fed, individual fish temperament, and other tank mates all play a part. I have had a flamebacks in the past and mostly they were model citizens. On occasion there were small chases, but that can be expected with any hierarchy in the animal kingdom. Nothing significant ever came of the minor chase.
If your going to mix with other angels you will want to consider difference in size, color, and shape. The greater you can separate each of these variables the more apt you are to succeed, at least I feel.
Personally I think the flameback is a wonderful fish, but so is the flame angel. Good luck!