Food allergy, sensitivities or intolerances are very commonly connected with itchy skin in dogs.
Chicken, beef, lamb, corn, soy, wheat, egg, and dairy products are common ingredients which induce these sensitivities.
The key to choosing a food for skin problems is to
- pick one that does not include any of these ingredients
- is preserved with vitamins
- preferably is supplemented with fatty acids (oils)
You could try a food with more novel proteins such as kangaroo or salmon.