I think your budgie needs to see a veterinary surgeon so that he can be checked over regarding the skin problem. If you have not registered your pet with a vet already, there is a list of local ones ...
Here's how to give your budgies their first bath, easy budgie bathing training, no wasting of time and money getting fancy expensive plastic products, here's how to get it done effectively, and where ...
My budgie always refuses to go in the bath and recently his skin has become flaky and he scratches a lot.