Have you thought about your dog maybe being allergic to chicken? My dog is allergic to chicken and gets really red and itchy if she has it and gets stomach upset. She's not allergic to duck and has done well on the DVP duck formula before, but you were adding chicken to the food to try and add protein.
It's really not necessary to add meat on top of the food. DVP Natural Balance is low in protein but it's not low enough to be a health issue.
I would just give the kibble for now because adding meat on top of that could be making the stomach upset worse.
If you want to add meat maybe try an a meat other than chicken. Venison and buffalo are good because they're not very rich and are low in fat.
Maybe you could actually have an allergy test done. Some vets don't like them and swear they're not accurate but other vets have had very good luck with them, so it's worth a try