How fast does your dog eat? None of our dogs have problems with gas, but one of them does burp a lot. Both gas and burping can happen because of excess air in the body, so eating too fast might be the problem. We have two golden retrievers and a beagle. One of the retrievers is literally finished with her food before the beagle even takes a bite. (Out beagle eats unusually slow, but that's another story.) We think this is why she has the endearing habit of burping in people's faces.
If you think he might be eating too fast, try putting some large rocks in his dish. (Make sure they're big enough so he can't eat them!) He'll be forced to slow down if there's other objects in the way of his eating.
I do think it's very possible that the food is the problem, though. It's kind of like how a lot of people have problems after eating beans, you know? Try switching his diet to another hypoallergenic food. We feed our dogs a rotation of foods, and as long as we get high-quality kibble, they do fine. We have a different health problem with one of our dogs, but we've found that the more natural a food is and the less preservatives it has, the better.