Yes, you can use flaxseed oil to help your dry eyes because flaxseed oil is rich in Omega-3, which is very helpful for reducing dry eyes. This has been proved by American scientists and you can try that. What's more, fish oil, also contain important dietary fatty acids which have multiple health benefits has the function of preventing and controlling of dry eyes.
Flaxseed oil has lots of utilities, it's always used in antitumor agent, and it can improve our nerves system, it also can reduce our inflammation and make our cells work efficiently.
So it can help you to get rid of dry eyes in a certain degree, however, you'd better use eye drops.