Hello and welcome. My name is Scott and I am an experienced small animal veterinary surgeon, I will be very pleased to work with you today and will try my best to answer your question to your satisfaction.
Tell me have you tried anything to treat your dog's coat so far? Is this at all itchy for your dog?
no there is no itching
ialso give it cod liver oil
That's good there is no itching, that usually rules out mange and allergic skin disease. There are a couple of things you can try, an obvious first thing is to use human head and shoulders shampoo on a weekly basis until you see a difference. This is actually often quite effective as it medicated.
There are in fact very few drugs which will directly affect the skin in this sort of condition, but one such is thought to long chain polyunsaturated fatty acids. Dog show people often add this to their dog's diet as a supplement using commercial products such as Mirracoat.However a very good source is healthy margarines such as Flora which are rich in polyunsaturates, over the years my clients have often reported very good results by adding a couple of teaspoons of Flora to the dog's diet each day. It takes about a month to exert its effect but you most likely have this type of margarine in the fridge anyway. This can often restore the coat to a very glossy condition.
If the above measures fail then the dandruff can be due to a low level dermatitis, in which case antibiotics from your vet may be needed. It is always a good idea to have your vet check things over if the coat does not respond to simple measures as sometimes there are other underlying diseases.