If your dog is highly allergic to chicken then even though the chicken was hydrolized in the food it might have still been too much for his system. I know 2 dogs like that, chicken, no matter what form it's in, sets off major reactions in them. That might be what's going on and why the food did not work.
Have you considered home cooking for him for a month, doing that you'll know exactly what he's eating, and can par it down to just a couple of ingredients. I'd suggest something like 1/2 meat (make sure it's something he hasn't had like maybe pork) and 1/2 quinoa. I suggest the quinoa because it's novel, not a grain, and is considered a super food. If he does better you know for sure it's the food, if not then it's likely environmental.
I'm not sure if you knew or not, so I'll mention it, when doing a food trial it's important to only give the dog the trials food and nothing else, no chews, no treats. If you must give the dog treats make sure it's the same ingredients as the trial food. What a lot of people do is simply use the protein type (fish, chicken, pork, beef, etc) as the treat.
What I'd also do is wipe him down whenever he comes in from outside, especially his paws, legs and underbelly. That should help to cut down on any environmental allergies that he may have.
He could be highly allergic to fleas, I've seen flea allergies cause that type of reactions
If you really suspect environmental allergies an allergy test might be worth the money.