Fish oils are recommended because they are a source of the longer chain fatty acids such as DHA and EPA. Your body doesn’t synthesize these from the type of shorter fatty acids you get in flax oil. If you get cod liver oil, it’s also a good source of preformed vitamin A (meaning you don’t want to take too much of it). Other types of fish oil usually have little to no vitamin A. Fish oil is a bit expensive, but you don’t need much of it to get your RDA, which is 1.6 grams. Also, personally, I’d recommend improving your omega-3/omega-6 fat ratio by lowering your omega-6 rather than increasing your omega-3 much.
If you want to know what mix of fats your really should use, I hate to say it but the recommendations on what fats you should get is a mess of conflicts and controversy, probably more so than any other nutrient. The NIH recommends 17 grams of Omega-6 and 1.6 grams of Omega-3, which is an omega-6/Omega-3 ratio of over 10:1. But there’s abundant research that a ration of under 4:1 has numerous health benefits. To improve your ratio, some people recommend you should up your omega-3 consumption, but there’re risks. It is known, from multiple studies, such as studies of the inuit who have high levels of omega-3 consumption (because they eats lots of fish) that high omega-3 levels slow down blood clotting, and thus can increase your risk of certain types of heart disease. Other people think, on the other hand, that it’s the recommendations on Omega-6 that are seriously inflated, and they recommend getting closer to 2 grams per day.
To add even more controversy, there’s disagreement on saturated fats. The NIH thinks you should consume as little saturated fat as possible, meaning you’d get as much as 70% of your fat as monounsaturated fat, and there is good research on the benefits of a mediterranean diet, of which high monounsaturated fat consumption is one component. But others think that your saturated fat consumption should be much higher, closer to 50%. They base this on, for example the content of breast milk above and on historical data on certain cultures with high saturated fat consumption and low heart disease rates. They also criticize past research because researchers failed for a long time to distinguish naturally saturated fat from trans-fat.
Suffice it to say, the NIH represents the most popular opinions on fat, but recommendations have changed on this have so much over the past few decades that it’s probably safe to say that they will continue to change. I suspect the omega-6 recommendations are seriously inflated and that the risks associated with a diet high in saturated fat are in error, but I’m not a doctor, so take my opinion with a grain of salt.