Sounds like plain old dandruff to me. Brushing should help sort this out – stimulates blood flow to the skin and gets rid of dead skin cells. Also, dandruff can be caused by a mild food allergy, you may need to take a look at what your dog is eating. Some fish oils in the diet would be a good idea too, works very well with some dogs.
There’s a great skin shampoo called dermocanis you could use. Its a skin wash and expensive for a shampoo but it works! The coat and skin is spotless after use. You shampoo it in and leave for a few minutes.I think you can only buy from a vet.
If there is dry skin in existance then there is an underlying problem.
Shampoo will only mask the symptoms.
You need to look at diet first……..usually the root cause.
Dont mask the symptoms with a shampoo get to the root cause.