What is the healing/recovery ability of an American Five-lined Skink?

Indeed, it is illegal in most states to remove or even touch wild animals, so I don't recommend taking it to the vet and trying to pass it off as your pet. Their healing ability isn't any more special than most other reptiles; they can't regenerate body parts aside from their tails, and wound-healing will be the same as most other reptiles. I'm not sure if this one is actually trying to "chew its leg off," but it probably knows what it's doing in any event. It might actually be licking the wound to keep it clean. It's unfortunate that this animal seems to be suffering, but there's not really too much you can do for it (unless it's on death's door, I wouldn't recommend euthanizing it either).

EDIT: Unless you were to try and pass it off as your pet, you basically admit to breaking the law. You are also gambling on the fact that the vet even knows what the animal is, let alone how to treat it.

just keep it in a tank give him a dish with mater and throw crickets so he eats and he will recover in front of your eyes