Don't use flax oil or any omega 3 fatty acid for high heat cooking. It will alter the chemical properties and you will not receive the same benefits.
For high heat cooking, some sort of saturated fat would work best, especially on a CKD. Butter, coconut oil and the like come to mind.
Use the extra virgin olive oil combined with mixed nuts/almond, cashews, macadamias, peanuts, filberts pecans etc. as a good source of clean fats in addition to flax/fish oils. These all have fairly high monounsaturate content which is healthful and does not hurt your ratio of omega 3's to 6's. Olive oil is virtually all monounsaturates as are macademia nuts.
I like to go for about 6 grams or so combined EPA/DHA per day. I have seen estimates that about 25-35 percent of the omega three oil found in flax is converted to usable EPA/DHA in the body. That is why it is a good idea to use a combination of flax oil AND fish oil or a fish oil supplement to help meet daily needs.
The reason a lot of people chooose to supplement with flax rather than fish oil alone is that flax oil has many health benefits that you can't get by only consuming fish oil. The two complement each other well to provide an excellent omega 3 spectrum.
-Blade