We had a dog when I was growing up that would have awful gas every time we changed foods. It was particularly bad when the change was from higher to lower quality (we were a bit financially challenged at the time).

He also had some other issues that I now think involved food allergies - the whole paw-chewing thing. It was pretty bad. I asked my mom about it more recently, and she agrees that the symptoms fit for food allergies, but we never had a vet confirm it.

I do know that when I (and my now-ex) adopted a shelter dog, that feeding medium to high quality food made a huge difference in the smell - she stunk to high heaven when we adopted her (both gas and just a smell coming from her skin...like doggy B.O., even though they don't sweat!) I now feed Nutro Natural Choice and am happy with the results. I started out with the 'sensitive stomach' one - chicken and oatmeal, I think, and now I change it up between chicken/rice and lamb/rice. Belle loves all 3 flavors (was always really picky with the cheaper food-hardly ate any at all), and I haven't had any other stomach issues with her (including car-sickness, but that's probably not related). It doesn't seem to mess her stomach up at all to change between these foods, as long as I keep the quality consistent.