No
Chicken is fine for them!! Unless they're allergic to it. One of my furbabies gets chicken in her homecooked meals and we have no problems at all
In fact, when a dog is having tummy problems, the vets usually put them on a bland diet like boiled chicken and rice, no seasonings or anything. I haven't tried this particular diet that you're speaking of, but I think you have nothing to lose. I pray that this is the answer to your furbaby's problems