The subject of fats and oils in our diets is challenging: what we “know” one year (e.g. butter is bad for you) is found to be untrue several years later. My general advice to pet owners is to feed a good quality complete diet, but is there a place for oil supplements for pets?
The science behind this is complex enough, with loads of TLA’s (Three Letter Abbreviations), making it difficult to understand and remember.
Wikivet have written a simple summary of the story behind fats and oils in pet diets. Basically, Omega-6 and Omega-3 oils are essential fatty acids (oils) that pets must have in their diet, as they cannot manufacture these in their bodies. The visible consequences of a diet low in these oils is a dry coat, perhaps with flaky, itchy skin.
Simple vegetable oils (eg sunflower) are a good source of Omega-6 fatty acids, and most commercial pet diets contain reasonable quantities of these.
Omega-3 fatty acids tend to be more expensive: flaxseed oil and fish oil are good sources. They have an anti-inflammatory effect which can be helpful with many types of skin disease, but it’s important not to give too high a daily dose.
Commercial pet food producers have to follow guidelines on quantities and ratios in pet diets, so it’s more likely that issues will be seen in practice when pet owners are feeding home-prepared diets that may not include sufficient supplementation.
What should pet owners do? If your pet has a shiny, healthy coat, the chances are that you are already feeding a diet which is adequate in fatty acids. If not, then talk to your vet about changing the diet, or perhaps giving daily supplementation.
Please note that I am unable to answer veterinary questions in comments. If you have questions or concerns about your pet's health it is always better to contact your vet.