Salmon oil, with its valuable omega-3 fatty acids has many benefits for dogs, and virtually no side effects.
Some medical research suggests that excessive levels of omega-6 fatty acids, relative to omega-3 fatty acids, may increase the probability of a number of diseases and depression. Modern Western diets typically have ratios of omega-6 to omega-3 in excess of 10 to 1, some as high as 30 to 1, partly due to corn oil which has an omega-6 to omega-3 ratio of 49:1. The optimal ratio is thought to be 4 to 1 or lower.
There are many source for Omega 3, like flaxseed also. but since being plant source it has more omega 6. Omega 3 is most in animal source, like fish oil. So for omegas my bet is that animal source is the best.
Diet go for good food like Taste of Wild ... Giving inferior food cause several issues like poor skin, infertility, thyroid to name few.
Rest as it suits you.