I currently have 3 angels in my reef (mixed with lps, softies, zoas, sps, clams, etc) and the current cast does not nip (that I have seen). I have a flame, pygmy cherub and bellus. I have had a couple of Regal angels as well but my luck is bad with them as they are very very hard fish to keep. In the past I have also had coral beauty's, rocky beauty, lemon peel, black nox and a watanabei.
I will say that of all the angels that I personally have had flame angels are the worst nippers. Flames are my wife's favorite fish so I had to have one in my current reef. I went through 4-5 flames before I got one that didn't nip. Every one I had nipped at SPS and fleshy lps. Just have a fish trap ready and be prepared to take it out since they are more likely to nip then not.
Also, IMO fish do not nip out of hunger, they do it out of curiosity and instinct. I feed my tank heavy, 3 times a day, this does not deter nipping.