Your flame angel and the Coral Beauty fight. I also noticed that fish like to act more aggressive when you are not around and not looking at your tank. Watch them from a distance, hidden, and see what causes the ripped fins.
I personally think that it is the flame angel, they tend NOT to do well with any other angel, as they are too territorial and the other angel, will die... unless you remove one of the angels. When it comes to flame angels, don't keep them unless you have a giant aquarium with a lot of territorial space.
So do this, remove the flame angel and put her into a separate SMALL tank. Let the coral beauty heal up (month-2 months) and that will also allow her to establish her territory. Then once you see that she is healthier and stronger, you could put the flame angel back in, but I would recommend for you to sell her... small tanks are bad for flame angels.
I also would say that the clowns don't touch angels or ANY other fish, except clowns of their own, or different species. Leave the clowns alone... focus on your flame angel.
Also please tell me your order of introduction that you had... what fish came first, what came last... What is your tank size, are your rocks full of holes or they aren't... all of this accounts for aggression...
EDIT: This is probably NOT fin rot, because I see 'bite' marks on her anal and dorsal fins... fin rot typically has tissue discoloration around that area :: her tissue around the damaged area contains its color, so this MOST PROBABLY isn't fin rot.