Hello and welcome to the forum. Has as been said, finding something suitable can be trial and error. You want to be looking for food with oil/s and no red ingredients.
All dogs are different and this may, or may not help but FWIW I will share the experience of one of my own dogs. She had a long standing skin problem - it was dry, itchy and she used to have occasional hot spots where it would break down. I tried various products including a short spell on raw food. Fish4Dogs didn't really suit her and I now think it is because she doesn't do very well with white potato. Also, she reacts to high cereal content products - I recall that her skin was terrible on James Wellbeloved Adult. I now stick to food that has either brown rice or sweet potato as the carbohydrate source. She is also OK with butternut squash.
I tried Yumega Itchy Dog and it helped. I also changed her to cold pressed food and was able to stop the Yumega Itchy Dog. She's been on cold pressed food for about two years now and her skin hasn't broken down since. The product that I use contains four types of oil, Evening Primrose, Linseed, Rapeseed and Fish Oil.
I agree that it's helpful to pay a lot of attention to grooming, particularly in the moult season. Whenever I bath my dogs (not often) I use Sebocalm and find it very good because it is gentle, hydrates the skin and is soapless. Would also recommend that you see the vet if there are any broken areas (usually done by the dog scratching) because bacterial infection can make things much worse. A course of antibiotics usually clears that up. Whichever product you change to, it will take a little while before you see any changes so be patient.