I don't know any vets in Knoxville that are in the retriever game so no one to recommend going out of your way for. Most of the time I go to Pet Well Clinic which doesn't charge you a visit fee, you just pay for the vaccines you need unless you want the vet to conduct an exam as well. You just walk in, they don't take appointments but I don't think I've ever waited over ten minutes and I think there is one in Alcoa.
There are some really good specialty vets at UT and some in west Knoxville if you ever have a specific need.