I didn't know oatmeal had moisturizing effect on animal skin. But if it doesn't work out, or you want to try something easier than shampoo, add some fat to her diet. Chicken or turkey skin has very good fat for dogs, as well as salmon oil which is slightly more expensive, but it has lots of great nutrients.
The scratching can also be allergy, Pinkle. Check if her skin doesn't seem red. Dogs are prone to developing food allergy if they eat the same kind of food for a long time. I think chicken and cereals are the most common allergens.