If he has been doing it for this many years, what may have started as an allergy related issue, may have turned into a behaviorial issue. Kind of like us chewing our nails and cuticles. It just becomes a habit and we don’t always realize that we are doing it.
I understand about the testing. It is pricey to determine what the dogs are allergic too, but that is the only way to come to a real conclusion and to find a solution. But, you may want to try eliminating the chicken treats from the diets. Common meats such as chicken, beef, and lamb are major sources for allergies. I think that the duck might be ok, but try to venture into the exotic meats, if you want to feed meat based treats. Stick with the fish and grain-free diet for a few months and see how that works. There are fish treats out on the market! You won’t get immediate results, hence why to keep them on a strict diet for a few months. A lot of it is trial and error. But, you do have to give each food time to “work” and allow the body to rid itself of the previous food allergens.
Yes, dogs with allergies is tough! My dog is an allergy girl. She gets Benadryl during the warmer months, and is fed an exotic meat and grain-free diet, along with canned salmon, sardines, cooked egg, and some cooked meats off an on. Sometimes real meat is better than processed meat used in kibble, due to the processing and chemicals used. Try cooking of some ground turkey, beef liver, tripe, or organ meat (will have to get at a local meat market/butcher). Sometimes that helps too.