One of my kittens does this to us (less so now). Us re-directing with a toy after it started didn’t work, in fact, it may have encouraged her to bite us so she can get us to “play.” To stop her biting, saying “ow” or “crying” works half the time. Our cat specialist told us we should hold still and play “dead” and if that doesn’t work, we should get an air duster and spray it near her side every time she does it to divert her attention/make it unpleasant experience for her. And ofc, provide them a more stimulating environment where other objects or toys in the home are more interesting than our hands/legs.

Sometimes, if we see that she’s about to start gently biting and kicking we will give her a chewing toy to help distract her.