Is it permissible to burn hair, bury it, or place it in flowing water to fulfill a vow made for a brother with autism who was cured?

This vow is not binding, so you are not obligated to do anything, neither to cut your hair nor anything else. However, it is preferable and more cautious to offer an expiation for an oath (kaffarat yameen) if your brother recovers, to avoid the scholarly difference of opinion.