I don't think that an oil supplement is really necessary if your dog is eating a well balanced diet. My boy's coat got all dried out over the winter, so I started adding a fish oil supplement. Not all fish oil supplements are created equally. If you do choose to add a fish oil supplement, make sure the supplement specifies what type of fish oil it is. Otherwise, you don't really know what you're getting. I use a Nordic Naturals Omega-3.
Nordic Naturals Omega-3 Pet Cats and Small Breed Dogs
That little bottle lasts a long time. A lot of people on YT have had good results with Nordic Naturals. They also make a Cod Liver Oil in liquid and/or capsules. You can get those on Amazon.