Sad to say, not all coconut oils have omega-3 fatty acids. Even if they do, it's only in trace amount. And it's ALA (alpha-linolenic acid), not EPA or DHA. Even if you choose the best quality unrefined virgin coconut oil it may not contain the ALA omega-3.
Which is why you don't see any refined or unrefined coconut oil brands labeling their coconut oil as a good source of omega-3 fatty acids. (Having omega-3 on the label is a plus and will definitely bring in more sales.)
Since we're at it, we might as well take a look at how much omega-3 fatty acids to expect in coconut oil in case it does contain. And also, the omega-3 to omega-6 ratio to see how close or far it is from the recommended value 1:4.
Let's zoom in on the polyunsaturated fats given by the USDA data on coconut oil since both omega-3 and omega-6 are polyunsaturated fats.
In 100 grams of coconut oil, we have:
|Polyunsaturated fat||1.7 g|
|Omega-3 fatty acid|
|Omega-6 fatty acid|
Using the data above, the omega-3 to omega-6 ratio is 1:84. Which is extremely off from the recommended 1:4. This shows that coconut oil is not a good source to provide you with the recommended ratio of omega-3 to omega-6 fatty acids.
Next, imagine you consume one tablespoon (14 g) of coconut oil, you would be ingesting only 0.0028 g of ALA omega-3. Even if you increase your intake to 3 tablespoons per day, it's only 0.0084 g. Which is very far from the recommended 1.1 to 1.6 g of ALA daily intake for adults.
Conclusion? Don't rely on coconut oil for your daily intake of omega-3 fatty acids. Even if you're lucky and happen to get one with a petty amount of omega-3, it won't help much in boosting your health.
To consume more omega-3, you can simply take plant-based softgels which directly gives you DHA and EPA. Or you can mix flax oil with coconut oil and add the liquid mixture to your meals and eat it. This way not only you'll reap the health benefits of coconut oil, but also you'll get enough ALA from flax oil for the conversion to EPA and DHA.