Hey Nick, I see things are going well for you, outside the recent "situation" of course.
This is an interesting thread, so I thought I'd offer a few thoughts.
Looking back, although it is difficult to determine what caused the death of the Flame and Coral Beauty, I think we can agree that stress was the primary factor. One thing about quarantine tanks that I always consider, is to not underestimate the importance of reducing stress. When you consider the experience a marine fish has, from capture to wholesaler to retailer to the home aquarium, is it any wonder that the marine hobby has a reputation as being difficult? Personally, I worry far less about creating a sterile environment and worry more about giving the fish a safe and secure place to settle in, get acclimated to my feeding behaviors, rebuild its immunity system, put on a bit of weight, and become confident and ready for introduction into the display.
I'm not saying anything you don't already know, but I guess my point is that I personally look at this thread and believe the decision to put the Flame and Coral Beauty together in the Q tank was the underlying cause. I suspect that had you purchased either one of these fish independently, assuming you selected a healthy fish, that the experience would have been much different. (Were the fish healthy at purchase?)
On another note, did you introduce an ammonia source when you cycled the Q tank? Or just a small piece of live rock to seed the sponge? If you only used live rock, using more live rock would have likely knocked this process out a lot quicker.
In terms of keeping any species of Centropyge angelfish together in an aquarium, they do best in male / female pairs, and can do well when kept with mixed species. Although I agree that keeping multiple species of larger Angels, such as the Holacanthus, Poaocanthus, and Genicanthus, is a bad idea. In fact, mixing any 2 large Angelfish, even from different genus, can be very difficult. But I have seen (and kept) many a successful display with multiple Centropyge species. The key is space, and I would generally suggest 50 gallons per pair when mixing species.
Hope this helps in the future. Go buy another Flame! They are easy to keep and very rewarding. Just realize that they are by far the most aggressive of the dwarfs! I don't recall your display tank size, but a mated pair might work best.