Feed him just white rice for a couple of weeks. There's absolutely nothing in that for him to react to. If it clears up while he's on rice, he's reacting to something in his food. Then put him back onto real food one by one to find out which he starts reacting to.
We feed our farm dogs a mixture of cheap dog biscuits, raw mutton (old or sick ewes that needed to be put down), and offal (we don't tend to get around to cooking liver, kidney etc so the dogs get most of that when we kill animals for the house). House dogs get cheap dog biscuits, table scraps and boiled mutton (less smelly in the house). But raw is healthier, and simpler. If you do want to feed them poultry, remember dogs can crunch up raw bird bones, but if you cook it you have to remove the bones as they become splintery, so if you just feed it raw you're giving them double the food value for a fraction of the work.
If you go to your local saleyards they're bound to have some small pens where they put the random sheep or goats that had to be removed from the main lines for one reason or another. Most people are paying full price for a pen of 100 animals, you go along and pay a fraction of that for the one that got injured on the truck, or the skinny one that jumped in and wasn't supposed to be there in the first place. Feed that to your dogs. Make sure you give them the offal also, very nutritious. Wild dogs etc will eat the offal out of their kill before they even start on the meat, they know that's the best part.