Has he had a fecal sample (or more) done to rule out parasites? (especially thinking of giardia or coccidia)
Chicken and rice may be fine for a while, but it will not be adequate for a growing puppy
First off, I think I'd find another vet who wants to find out the cause of the diarrhea. That is not normal in a puppy that young
In the meantime you could get some digestive enzymes, such as Prozyme to make sure he gets enough nutrients from what he is eating. I'd also give him some plain yogurt and some green vegetable baby food or pureed vegetables (green beans, spinach and peas are pretty well tolerated by dogs) Add it in slowly, a half to a teaspoon at first to see how he tolerate it, and add only one thing at a time.
So first the Prozyme, then if he's handling it well after a couple of days, then add yogurt (again a very small amount at first), then the veggies.
Best of luck