When you switch protein sources, how long before you see signs of improvement?

I'm pretty certain my Mastiff has a chicken allergy. I have switched him to Prairie Lamb and Oatmeal formula, hopefully to stop the itching and skin issues. I realize if this doesn't work, I may have to go grain free and that will be ok too. I just want to know for any of you that have had dogs with skin problems and have tried this----how long does it take to see results or how can you tell the new food is agreeing with your dog? Thanks!