My beagle used to lick and chew on her feet. You can tell if they have been doing it for a while if the hair around the foot is brown. She had allergies. We changed her food and she settled down. No corn, wheat or beef and she is fine. Sometimes things like rock salt in the winter or fresh grass or certain weeds will irritate their feet. Wash your dog's feet in an anti-itch shampoo and dry them well, that helps if something is on their feet.