My Shih-Tzu does this as well. He has been licking, scratching and chewing his paws and his flanks since I got him at 10 weeks old and he is now over 5 years old. I've been to the vet numerous times, had all the allergy tests done, had him checked for fleas, eczema etc etc. Nothing has been found. He is otherwise a lovely, well balanced and very happy little dog. He has just always had itchy skin, no pink irritated skin, no infections, no flaky skin, just itchy skin. My vet finally come to the conclusion that it might be the food coloring in the pet food, so we tried various that don't have any. No change. Still love him to bits though!