While it is tempting to try differnt shampoos and foods, I would take it one step at a time and eliminate one thing at a time. This way you can see what might be the trigger for his itching. Switching foods may not show results right away so don't give up on it.
Hot Rod loves chicken and we never thought anything about it, until recently when he hadn't had any for some time and then we started to notice him licking and chewing his paws a bit more after we gave him chicken (we were eating it more and they each get a small niblet from us after dinner). We stopped giving it to him and then gave him some again and the chewing started. When Hot Rod first came home, he had such flaky dry skin and his ears were terrible-big flakes of skin would come off!
Thinking back...most puppy food has chicken. We tried different shampoos and salmon oil, etc. We even have medicated shampoo and medicated conditioner from the vet (which did and does help-I didn't use it for a month -2 bathings worth and noticed some flakes). We are slowly reintroducing poultry - right now he's been eating turkey and has not had a problem. I want to try chicken again just to make sure but waiting for a little bit yet.
I know how tempting it is to switch products but patience will definitely pay off. Trying a different shampoo can be a quick fix for the initial. How often are you bathing? Could the air in your home be drying? Do you have a humidifier? This could be another factor. Good luck.