Thank you for bringing this subject up Chris. I too have been thinking about this recently because one of my lot had her coat stripped back in August. Since then, it has failed to regrow and looked dull and lifeless. She was on a complete raw food diet. Long story short, about 6 weeks ago I put her back on the fish based dry diet that she had as a puppy (she had a beautiful coat then) and it is already showing a marked improvement. It is now growing, thickening up and has developed a shine that wasn't there before. I've concluded that it's a good thing to include fish (hence omega oils) in a dog's diet.
I'm a bit puzzled about supplementing with salmon oil or similar because a lot of the good quality foods already have added omega oils and you don't want to overdose if the dog's food doesn't have it in already.
According to this article
not all omega 3 is the same and the correct ratio 6 to 3 is important. Also, not all omega 3 is the same:
It is the DHA and EPA forms – found mainly from marine sources, which are beneficial. The ALA form of Omega 3 found in vegetable sources such as Flaxseed oil or Linseed oil must first be converted to EPA & DHA for it to benefit, and dogs lack the enzymes to do that efficiently.
As for ancestral dogs, I don't consider it because our domestic dogs have evolved and have much longer lifespans. I'm not sure we should use it as a yardstick for a dog's nutrition but I know lots of folk disagree. However, my breed, which originated in the Highlands of Scotland would indeed have been fed a crofter's diet of lots of fish, plus oatmeal, potatoes and vegetable/table scraps as available. Oddly enough, I've tried lots of products on my lot and found that a plain, fish diet works best for them.