D.B.
You don't say how a 10 year old is getting Flamin Hots without your involvement. Why is this food in the house? If you or other adults aren't buying it, how is she getting into stores with money to buy them without your help or acquiescence? It's time to stop advising her and start taking control. If this food is in the house, that has to stop, even if that ticks off other household members. Kids go through growth spurts and can put on weight quickly for a lot of reasons - you don't say the time period for the 25 pounds so it may or may not be all due to what she's eating.
If she is bipolar, that doesn't mean she's immune to rules and structure. There's a huge nutritional factor involved in various forms of depression, mental illness and behavioral issues. Food cravings can also result from an internal imbalance. It's actually the body's natural desire to add nutrients, but if we grab the wrong things, we don't solve the problem and we make it much worse.
I work in the food science field, and we are seeing huge results with nutritional breakthroughs and current research, with pretty rapid positive changes when the balance is restored. A lot of kids get especially quick results, and we are seeing all kinds of things like bipolar, autism, Asperger's, ADHD, PDD-NOS and sensory issues start to turn around in as little as 2-4 weeks. It's incredibly simple if the parent is consistent. Happy to help you more.