It sounds like your dog's skin problem may be rather serious. While fatty acids and other nutrients such as vitamins A and E, zinc, and protein do promote healthy skin and coat, there are many factors that cause skin conditions that may require treatment beyond supplementation. We strongly recommend having your dog evaluated by your veterinarian, who can evaluate this condition and recommend the appropriate treatment.
Also, a balance of both Omega 3 and Omega 6 fatty acids is important, so supplementing one or the other may not achieve your desired results. Since high-quality premium brand pet foods are already well-balanced with these nutrients, they typically do not require further supplementation.