Are Omega 3 and 6 destroyed by cooking?

No, the Omega 3 and 6 essential fats survive the gentler cooking process typically used for eggs, such as scrambling, poaching and soft boiling. However, gentle frying would see a small loss. Prolonged very high heat can cause fats and oils to oxidise, but you are unlikley to be able to achieve this with eggs with any of the usual cooking methods. Eggs are delicate and should be cooked gently for best results.