We are dealing with this, too
I think for us, it's a combination of yeast and anxiety. The scratching/chewing starts off innocently enough, but then it turns into a compulsion (at least for our boy.)
Here is what we are doing, and maybe it might help you. Granted, he has a yeast infection, so we switched him to a grain free food with no potatoes or chicken (Canine Caviar Wilderness ALS.) In his food, he gets a probiotic, fish oil, vitamin C, and benadryl. He is getting bathed 1-2x a week with antifungal shampoo (you could certainly skip that.) We also mixed up a solution of organic apple cider vinegar "with the mother" with water and use this as a 'rinse' that we rub into his skin (don't use this on any open wounds.) For open wounds, we use a bit of Vetericyn. We really try to discourage him from itching and chewing. If we catch him doing it, we will distract him and give him a toy or bone to chew on instead. He may have to go into the cone of shame soon
Have you done full allergy testing with him yet or is that the vet's hunch?