It depends on your fish and your aquascape and most importantly your luck.
I have a flame angel, a lemon peel angel, a golden angel, and a bicolor angel in the same 100 G tank. I have a lot of live rock and there are lots of hiding spaces/caves. I introduced all 4 at the same time. I knew I was taking a risk, but a buddy of mine had done the same with no problems so I thought I would give it a try since I was desperate for something to eat the majanos.. The lemon peel and the bi-color fought for a couple of days, but them the lemon peel established dominance and they have been peaceful tank mates since. All my angelfish seem to get along quite well.
If your flame angel is well established in your tank and /or you don't have a lot of hiding spaces in your tank then I would say that the flame angel is likely to kill the bi-color. Keep in mind that for some reason, the bi-colors are very fragile in the beginning and many do not acclimatize well to life captivity. In fact, most will die (> 80%) . Once they become established however, they are quite hardy.
If I had to do it again I would probably not buy the bi-color. I keep hearing stories about how many of these poor guys die because of our hobby.
Check out the majestic angelfish. It is quite hardy, beautiful, and did the trick for me (granted it took 6 months before it even noticed the majanos, but eventually it got the job done)
good luck!
sam