They've been known to nip at corals, but in general they should be fine as long as you keep them fed. They're not big and strong enough to do any real damage to most corals. I had a coral beauty angel and he never looked twice at a coral.
True - this is a "reef safe with caution" type of fish. Still, I think they're pretty safe in most cases. Certainly nothing larger than a dwarf, though.
I'd say coral beauty. I had a beautiful midnight angel who died after a couple of days due to ich. Also the blue one with the light colored face - can't remember what it's called. Never had the flame so I can't comment, though those are supposed to be in the reef safer section, too.
As Harpua said - nothing is 100% especially with angels. However most people I know have had very good luck with dwarfs or pygmies in their reef tanks.
Dwarf angels are find IMO. I have flame angel who nips everyday at corals, but not enough to damage them. The softies just shrink up for a few seconds and opens fully again when he nips them.
Its more dangerous for "larger" fish IME. Like my aurigia is not suppose to be reef safe, but he doesn't nip to strong (He's only 2-3 inches). My teardrop butterfly whose suppose to be semi is about 4 inch. and just rips them apart.