[anonymous]

For best results I would make an appointment with a board certified veterinary dermatologist for accurate testing, diagnosis and treatment.

Environmental allergies? Has mange been ruled out? Atopic dermatitis? Medical condition? Has lab work and skin testing been done?
Treatment is often a multifaceted approach. It’s not just about finding the right food, or the right shampoo, or the right supplement.
In fact the food may have nothing to do with his symptoms.

Do you have pet health insurance? You may want to consider getting it before he is officially diagnosed. Treatment can be a little expensive.
If it is environmental allergies, there is no cure. There is effective treatment, however it is lifelong, allergies tend to wax and wane so you may get lucky, they could be mild or seasonal (if that’s what he has). He could very well have some other skin disorder or medical condition that is causing these issues.

Bathing with a very gentle puppy shampoo at least once a week may help, but not if the skin is red, bleeding or irritated, in that case I would defer to the vet.
Talk to your vet, if you want to rule out food sensitivities ask about a prescription/therapeutic diet, that might be a good place to start, it depends on how severe his symptoms are and how uncomfortable the dog is.

I would go directly to the specialist if it was my dog, my dog sees a veterinary dermatologist once a year and has had a positive response to treatment.
She did well on Nutrisca salmon for years but is now on Zignature whitefish or catfish.
You could add fish oil (approved for veterinary use) once a day to his food, it’s supposed to help with dry skin. I add a little water and a topper, like a bit of scrambled egg (2 meals per day)