Have his previous foods all had the same protein sources (i.e. chicken or beef or fish?) If you're convinced it's the food, then I think you would have to try to narrow it down to what specific ingredient it is that's bothering him.
Also, how often are you bathing him? Bathing too often strips their skin and fur of the oils they need and can cause a great deal of itching and flaky skin.
The last thing to consider is that it might be something in the environment. Are you certain he doesn't have fleas? Could he possibly have an allergy to grass or pollen? Perhaps a lotion or product that you use on yourself which is then transferred to Brody?