Although plant-based products are usually sources of omega-6 fatty acids, there are vegetarian foods that contain omega-3 fatty acids as well. We’re talking about walnuts, flaxseed oil and olive oil.
Flaxseed oil is a good source of omega-3 fatty acids for humans, however not so much for dogs and cats. The thing is, flaxseed oil contains only a precursor omega-3 fatty acid, alpha-linolenic acid (ALA). ALA is used by human body to produce EPA and DHA (eicosapentaenoic acid and docosahexaenoic acid), which are the actual essential omega-3 fatty acid that we need from this. Dogs’ or cats’ bodies do not have an ability to transform ALA to EPA or DHA, so will hardly benefit from taking flaxseed oil the way humans would. So in this sense, dogs and cats are strict carnivores and flaxseed oil or walnuts are not suitable fatty acid food supplements for dogs and cats.
Considering that dogs can not transform ALA into the necessary EPA or DHA, we need to keep in mind that flaxseed oil is more rich in omega-6 fatty acids then in omega-3 fatty acids. As a result, it can not be used as an omega-3 fatty acid supplement, because omega 3 needs to be given to the dogs only as much as it has to balance out the omega-6 in the diet. So the whole purpose of fatty acid supplementation is undermined with vegetable oils. Same goes for olive oil as dog food supplement.