Obsessive licking like you are describing is often due to gastrointestinal issues such as intestinal parasites, IBD (irritable bowel disease), or food allergies. It can also be due to behavioral issues such as obsessive compulsive disorder.
It would be best to have him evaluated for the gastrointestinal diseases mentioned above. A simple fecal exam can evaluate him for intestinal parasites. If negative, it would still be a good idea to get him on a general broad spectrum dewormer. The next step would be to get him on a novel protein diet (a protein he has never been exposed to). This is available by prescription by your veterinarian. Some good formulations include Purina DRM, Hills d/d, Royal Canin IVD, and more. A food trial normally takes 6-8 weeks. This food needs to be fed exclusively, no treats
, no table scraps, no flavored toys or bones
, no raw
hides, absolutely nothing. We have to eliminate all other variables. For IBD, a novel protein diet does help in most cases, but sometimes steroids are needed. The only way to definitively diagnose IBD is with an intestinal biopsy. Since this is the most invasive test, I recommend deworming and putting your dog on a novel protein diet first.
You can also add some essential fatty acids to his diet. EFA's have natural anti-inflammatory properties and may add some moisture to the skin. Some good veterinary formulations include 3V caps and Derm caps. They both come in liquid, which would be best.
If this is behavioral, then anti-anxiety medications may be warranted. Talk to your veterinarian about all of the above mentioned issues and decide on a plan of action. Behavioral issues should be a diagnosis of exclusion, once all medial issues have been ruled out. This will help avoid misdiagnosis.
Good luck. Please let me know if you have any other questions or concerns.