I have a golden angel for 4 months and then I put multicolor angel for 2 month and then recently a flame angel on the same 155 gallon tank. The golden angel is a shy fish and did not do anything to muilti color one, but she chases the flame angel whenever she sees it. My flame angel lost a little bit of tail but is overall ok (I hope). When I feed only the flame and multi color come.
I have read couple ppl articles who successful keeping different kind of dwarf angels in the same tank by introducing the least aggressive one first and then more and more aggressive one later. I think the flame angel is a very aggressive one so I don't think it will do well with coral beauty unless you can introduce them at the same time. But try it and who knows, there is always exception in this hobby :-) Good luck
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