I have not had any issues with my flame angel. It seems of all of the dwarf angels, flame and coral beauty tend to pick the least, with dwarf angels generally picking significantly less than full-sized angels.
I had a coral beauty and rusty angel in my 120g SPS/mixed reef tank and they never picked at anything to my knowledge, everything grew prolifically.
29-34g tank is fine for a single angel with 2-4 other fishes, but they must be small. The angel is the largest of the fishes. It also picks all day at the liverock, so I would use fully grown-in liverock, ideally fresh from the ocean (though I did not start out this way, and mine went in pretty quickly). The angel I have now was also in a 34g solana with the other two clowns, and I believe another fish or two when I bought them originally from a hobbyist breaking down his tank.
I think the trick is keeping them well fed (though when I go on vacation I have someone feed once every 3-4 days, and have done this 4 times now without any issues), and keeping nutrients down through aggressive skimming.
I also have clams, a few softies (ricordia), plenty of LPS, but mostly SPS sticks, and have not noticed any of them being eaten by the angel. It does pick on the clam mantles now and then, but they actually don't respond much to it anymore. I would be nervous about their health from their lack of response, but they keep growing (can check the shell), so I think they're okay.
This is a great thread on people's experiences with angels in their reefs, and what they picked at. In a larger tank, one day I would love to add an Emperor Angel, it's one of my favorite fishes. But it needs >=180g tank.
Here's a quick thread on why and how you should QT new angels to keep them eating and happy as they adjust to your tank.