If a dog is allergic to a food, there's no point in ever reintroducing it unless you are trying to verify whether the dog is actually allergic to that ingredient and this is under experienced medical supervision by a vet who knows how to treat allergies. Otherwise I would consider this a pretty bizarre thing to do -- would anyone try and probe how much peanut or fish it takes to cause a reaction in a child known to be allergic to peanuts or fish? Surely this would be seen as at best, cruel and extremely uncomfortable for the child, and at worst, potentially fatally risky. So why do this with a dog?
It often is fairly easy to find out what causes allergies -- elimination diets are widely used -- but they do take time. A week or two isn't long enough.
I think most supposed allergies are simply sensitive digestions that seem to settle themselves within the first year of a puppy's life. This board is full of people who had puppies with tummy problems, all of which went away by the time the dog was one. If the problem is chronic and uncomfortable for the dog then it is worth taking the time and effort to really check properly for allergies. Chicken is in all sorts of dogs foods and treats so it really requires vigilance to remove it from the diet; same for grains. I wouldn't be concerned about poultry sources in a reputable food, but cheaper foods that might say they are a 'flavour' often have two or three meat sources listed in the small print or something vague like 'poultry meal' or 'meat derivatives.' I always look for named protein sources.