Basically, oils have good fats for you and your dog.. both internally and externally.
Here's your guide to oils in general.. we use Linseed/ Flax and Canola because of their relatively high Omega 3 and then 6 fatty acid count.. the oil is unsaturated fat too: so much better for pancreatic dogs...
If you feel you need to supplement, and want to get onto the coconut oil band wagon, please consider the origin of the coconut oil.. your dog may get a great coat: but child labour, unpaid poverty and 3rd world countries may feel the butt of your 1st world dollar...
The oils we use are produced in Australia: another reason to use them :)
For a really indepth look: I thing this page sums it up nicely...
Olive oil: A great source of monounsaturated fatty acids and polyphenols, which may be beneficial to heart health. personally I see dogs get diarrhea from this oil: so we use it externally rather than internally for skin issues: just rub it onto the affected/ inflamed spot twice a day.. a really cheap way of getting moisture into the skin.
Avocado oil: A great source of monounsaturated fatty acids, vitamin E and may even help to boost absorption of carotenoids and other nutrients. BUT.. make sure the oil comes from the squeezing of the flesh: no pith OR skin OR bark.. only the flesh! the rest is toxic to dogs. ANYTHING avocado based is toxic to birds, and horses and goats.. so keep this well away. personally, if you're having some in your salad: give a bit to your dog instead of spending loads of $ on the oil! .. it''' be made in Australia AND seasonal!
Flaxseed / Linseed oil: Contains both omega 3 and omega 6 fatty acids; it contains essential fatty acids alpha linolenic acid (ALA) that the body can convert into EPA and DHA, which are also the essential fatty acids found in fish oil. The reason we add the oils last in the meals, and cold, is because this oil is so high in Omega 3's , it has a very low smoke point, which means it goes rancid when cooked/ exposed to heat. it is an unstable oil so needs to be kept cool :)..It is one of hte highest oils in Omega 3's.. so if your dog doesn't liek fish: this is a fantastic dietary source of the essential fatty acids.
Macadamia oil: DO NOT FEED. THIS IS A HIGHLY TOXIC SUBSTANCE TO DOGS
Sunflower oil: Made of mostly polyunsaturated fatty acids and some monounsaturated fatty acids too. It contains vitamin E: sure.. but is still pretty high in saturated fats for me.. I'd rather feed the whole sunflowers to horses... and there are more beneficial oils out there..
Coconut oil: Is primarily made up of saturated fatty acids with a small percentage of fat from medium chain triglycerides (same fats as avocados). Though largely comprised of saturated fat, unlike butter which has a comparable saturated fat profile, coconut oil comes from an all-natural source. Coconut oil is solid at room temperature due to the high content of saturated fats, and therefore needs to be heated slightly to liquefy.
this is why we don't use coconut oil: apart from the often ethical issues, it is unsuitable for many of the dogs we feed. Also, it has a very pervasive taste.. so ALL the meals would taste the same.. and when you add it.. the meal now tastes overwhelmingly of coconut... Save it for externally: skin and nails
Rice Bran Oil: One MAJOR problem with this oil is its ratio of omega 6 to omega 3. Rice bran oil contains high amounts of omega-6 fatty acids (linoleic acid) -- and virtually no omega-3 (linolenic acid). This fact alone is enough to strike this oil out of your dogs diet permanently unless you are supplementing with omega-3. The ideal ratio between these two fatty acids is 1:1 and the nutritional habits of most people in developed nations has this ratio soaring more than 15:1 (Omega 6: Omega 3). So unless your dog is are consuming reasonable amounts of Omega 3 in their diet (basically Salmon, Mackerel, Sardines), you should stay away from this oil.
It does however have great fibre properties.. so if feeding a low vegetable/ grain diet, you could add this to your dog's meal to increase fibre in the diet... I'd use the actually oat bran, rather than the oil though.. always better to use the wholefood than the product from :)
Also, the majority of rice bran oil on the market is NOT cold pressed and some may be chemically extracted using solvents, in particular petroleum-derived hexane and high heat. So buyer beware of your source.