I think I can offer a unique perspective on this. I'm a coach and do gymnastics recreationally (3 hours a week) as well as long jump (track and field, 2 hours a week). I'm of course, older than your daughter and maybe have had more time to put stress on my ankles, but your daughter trains far more than I do and I think that narrows the difference in our situations.
I have had recurring ankle pain for about a year now and have worn ankle supports, tensor bandages, KT tape, athletic tape and likely anything else you can come up with.
First thing I'll say is in response to the mention of pain than flipping. Gymnasts train through pain often, rips, floor burn, whatever it may be. They love the sport and will do that whenever possible. I know I do. I never took a day off or ended early because my ankle hurt. So, I wouldn't suggest dismissing the claim of pain solely based on that behaviour.
Next, ankle supports. I think it wouldn't be a bad idea to buy her ankle supports. They will not save her ankles in any situation but personally I use just one on my right ankle and I feel more confident in my use of it as I always feel weaker in that ankle and the extra support evens it out. Careful, though... ankle supports can be quite restricting!
The best support for the purpose of support in my experience is the lace up, figure-eight velcro support. (
Link Removed). This support however, is the most restricting I've used. I'm not sure I'd recommend it for a gymnast, it may be suitable for some events but not all.
The best support I've found that is a happy medium between no support and too restricting is a less popular style:
Tensor Sport Ankle Brace, Home Medical | Walmart Canada Online Shopping
This support is very adjustable, comfortable and feels supportive but not excessively restricting. It's the one I use now while coaching, tumbling, jumping and sprinting. Another plus side is it's cheaper than the other.
Other options:
KT Tape (Kinesiology Therapeutic Tape): This is a stretchy fabric tape that is applied to support ligaments, tendons, muscles without restricting movement. The effectiveness of this is a debate but I stand by it's value. Could be psychological but I always have a roll on hand. It is easy to learn how to apply and stays on quite well (except in the pit!). Also, I'm allergic to some athletic tapes, not this one!
Generic White Sports Tape: Allergic to a number of these. A good method but very wasteful and expensive plus not all that comfortable if you tape the ankle the generic cast-ressembling way. I learned a method from another coach that proved quite effective, much less wasteful, restricting and irritating. I can explain this way if you need me to.
Tensor Bandage: Don't recommend. Hot, sweaty... okay for post-practice recovery but doesn't stay on too well while tumbling and the compression isn't always all that helpful.
Wow, took more time on this than I anticipated, hope this helps!