I learned something in one of my art classes in high school that helps with art. This technique realeases chemicals in your brain to actually calm you and clam your shaky hands.

If you inhale through your nose and exhale through your mouth VERY slowly as if there was a candle infront of your face you are trying not to blow out. Do this a couple times, with deep breaths and you should at least notice a difference, so try this a couple times before you fly.

Also relax and enjoy the flight. Just ignore it and it will go away.