Yes, if the food isn't offering enough oil, sometimes a supplement can help. Fish oil is excellent, but first make sure you are using a shampoo made for dogs, and a conditioner. Also, make sure you rinse the skin thoroughly after shampooing, the number one cause of dry flakey skin is improper rinsing. There are many good shampoos out there, but since Yorkies are bathed much more often than other breeds a quality shampoo that helps to protect the skin is important. I like Biogroom products and if you email the company, they will send you some product samples.
Bio-Groom - Exceptional Pet Care Products for Over 30 Years My little foster had white flakes coming from his skin and it took several months to get rid of it.