Sorry to hear about your dog. There could be a variety of reasons for this. Did the behavior just start or has your dog done this for a while? Have you treated your yard or home with any chemicals that he might be getting on his feet and irritating him? I found the link below that might also help. Hope everything turns out okay!

I agree with Molly. If it keeps up you might want to have your dog checked out by your vet to make sure it isn't something more serious.

Dog have a leisure time fun habit for licking there paws and they do not have nay such particular intention for that. They can't scratch there legs as we humans can do and the only thing they are left with is licking them to remove the itching condition. They might also do that in case something sticks to that.