A friend of mine has a Pit Bull – Boston Terrier mix that she adopted about five years ago. Malley is about 6 now and from the time she was adopted at one, she had issues with throwing up. Since she was very timid and nervous, it was assumed that she just threw up from nerves. After a year or more, when she was well settled in, it was still happening. I suggested that she had food allergies and to change to a no corn, no soy food. Malley did 
okay on it for a while and then started throwing up again. By trial and error, a food has finally been found that Malley has no problems with. As it turns out, nearly everything bothers the dog, from beef and pork to corn, soy, wheat and most other grains. She does okay on chicken and turkey, but does best on fish. Malley is finally on Wellness Fish and Sweet Potato formula.
I helped her work through different brands and formulas until the right product was found. Throughout the whole process, I have determined that the best place to start when your dog has obvious signs of food allergies is to go straight to a limited ingredient product such as Wellness. A product with one source of meat and one starch source is your best bet. Fish is the most non-allergenic meat. Sweet Potatoes seem to cause very little food reactions in dogs and are a great source of antioxidants and other essential nutrients.
Not that this formula or Wellness in general is your only choice of course, as there are many brands on the market. Just be sure you check your ingredients and feeding rate to choose the most economical brand for the quality desired. Stay away from by-products and long ingredient lists. By limiting the number of ingredients you put into the dog, you greatly limit the chance
of a food allergy reaction. If you have a reaction, you can very safely assume it is one of the two or three ingredients on the list. Then you can search for another product without one or all of these ingredients until you weed out the one that the dog is allergic to.
There will still be vitamins and minerals and probably a secondary fat source in the food also, but these are generally low reactions ingredients. Just stick to one meat and no more than two other main ingredients to sort out your issues.