Any idea why my dog likes to kick his feet back?

Dogs will also kick at the ground when they’re finished with their business. Perhaps he doesn’t like your furniture?

It’s scent marking. Dogs have sweat glands and scent glands on their feet.

My dog lays on her back and pushes herself around the floor while using the couch as the kicking spot all while snorting lol I think it’s her own personal back scratcher!

Yes I agree with @crisw – they are scent marking.
We have two dogs and I think she is showing her dominance in this situation.

I agree with the idea that he’s scent marking. My cats do something similar – they rub their snouts on things. (Not really their snouts, but the sides of their mouths where their cheeks would be.)

My cats’ water dishes are kept on a plastic placemat on the floor, and my male cat will “scratch” the mat a few times before he drinks. I wonder if that’s scent marking as well?

Scent marking as others have said :)