What are the benefits to cooking with flax seed oil?

Possibly inflamation. Flaxseed oil is a source of polyunsaturated fatty acids such as alpha-linolenic acid. The alpha-linolenic acid and related chemicals in flaxseed oil may decrease inflammation. That is why flaxseed oil is thought to be useful for rheumatoid arthritis and other inflammatory diseases.
Best not to heat . The health benefits diminish when flax seed oil is heated. When purchaing flaxseed oil, it is quite important that it be cold pressed & not heat pressed. In general, flax seed can help to lower cholesterol & low-density lipoprotein levels & thus helps reduce the risk of heart disease.