[107barney]

Food allergies in dogs are rare, less than 10%.
The dog more likely has environmental allergies. Your vet can try the dog on antihistamines and treat any secondary skin infections w/ either medications or shampoos. If the problem persists beyond that, other things like steroids, combination medications, or certain types of immunpsuppressing medications for allergies can be used.
I would get a handle on the environmental allergies first. Most dogs do fine with the general veterinarian giving a course of treatment while others have complicated cases that might require a vet dermatologist.

Good luck!