People have done it with flax oil, I believe only once, and decided there is no advantage over other cheaper oils.
Of all oils, flax is the most unstable.
It goes rancid very fast. It should be kept frozen and in a dark, to extend the shelf life, but none of the stores are keeping it frozen. Some keep it refrigerated.
It is also much more expensive than olive oil, or any other oil.
Flax oil is the best with cottage cheese or with yogurt (budwig diet).