If it is his diet indeed, of which i am not sure because i dont have experience with long-coated dogs, I am always told that the best things for a shiny coat are fish, bananas and eggs. Especially very oily fish. Also I heard that bathing and washing the dog to much is not good, and low-fat-diets aren't either. I read a while ago about more people putting a spoon of olive oil in there dogs food. But i cant assure if this works or is very healthy, so if you want to try those things i would ask the vet first. Good luck!

This is one of the articles i found and that seem more reliable (don't overlook the other two pages belonging to it)
Dog Food for a Healthy and Shiny Coat on MedicineNet