Mordy said:
Yes, it's a very safe and healthy thing to add to a dog's diet, and it is more useable by the body than for example flax oil.
Just make sure you buy a high quality product that is free of contaminants, not watered down and doesn't contain any artificial preservatives or stabilizers.
Additional omega 3 fatty acids in the diet increase the body's need for vitamin E, so you should supplement with approximately 100 IU per 25 lbs of body weight per day. Make sure you get a natural vitamin E supplement, anytime you read "dl-alpha tocopherol" it's synthetic and far less effective.
Since capsules are often messy to deal with and not all dogs eat them willingly, I generally recommend buying a liquid vitamin E supplement that's easy to dose with a dropper.
Saying that fish oil is more useable than flax seed oil isn't true. The difference is mainly in the level of elongation of the fatty acids.
Flax seed oil, and nearly all plant-derived n-3 (omega-3) fatty acids consist mainly of 18:3n3 (linolenic acid). There is evidence that some mammals, including dogs, can convert this to longer-chain fatty acids, such as docosahexaenoic acid (22:6n3, DHA). DHA is the omega-3 component of fish oil that has recently been shown to be vital to neural function and learning, as well as cardiac health, etc., etc., etc.
In addition to long-chain polyunsaturated omega-3s, fish oil also contains other long-chain fatty acids like arachidonic acid (20:4n6, AA or sometimes ARA) and eicosapentanoic acid (EA, 20:5n3). AA has been shown to be more important to growth and EA has roles in blood clotting.
So if you want to use flax oil--that is fine, too. Fish oil will provide a full spectrum of long-chain fatty acids that your dog will either use or discard as waste.
You do NOT need to give anything to balance the omega-3 supplement, as animal-based diets are already very high in omega-6 fatty acids. These are compliments--too much omega-6 (very easy to obtain from normal diet) will create a deficiency in omega-3.