Since that food has limited ingredients and an uncommon source of protein, probably not a food allergy. Also, you didn't mention ear infections or constant paw licking which seem to go hand and hand with food allergies. The food you are feeding is salmon based which is an excellent source of omega fatty acids. I have heard that coconut oil can help with various skin problems and even flea allergies. This article states 1/4 tsp. per 10 pounds of body weight twice daily. I think I would try the other posters recommendation of coconut oil since he is already on a fish based diet. Hopefully, the coconut oil will work long term and you can just try the Benadryl for a short time until the benefits of the coconut oil kick in.
The Health Benefits Of Coconut Oil For Dogs