It depends what your dog might be allergic to. Do you know?
A York test or other similar blood test might be a good way to establish food sensitivities and you can work from there. However, that said, I have a dog that is allergic to pollen NOT food but I saw an overall improvement to coat, skin and general condition when I transferred him to a raw diet. Even if it had no noticeable external effect his new diet improves his health and wellbeing which in turn helps him to handle his allergic reactions better.
One of the things you might want to watch with a sensitive dog are the conditions in which the food is stored - grain based dog foods can have mites which may cause your dog problems.
This is an interesting article about the problem. Freezing the food may help in some circumstances