Although I've never cheered in the Nike Free cheers, they are modeled after the Nike free runs (which I run in all the time). They are a minimalist shoe and meant to be as lightweight as possible. So even though they are "modeled" after a sneaker, there is not very much to the base. I'm not sure how they would hold up on a hot track and if they would actually be thick enough. The Nike Stamina or Sideline might be a better choice.
I would look into the Team Cheer Cobra. It has a thick base and is a heavier duty shoe. Although I don't think it would be great for a lot of tumbling, its super affordable so you might want to try it out anyways.
Team Cheer Cobra | Cheerleading Shoes | Team Cheer