When children are scared of something, oftentimes the best way to handle the situation is to help them confront it. When that something is fear of flying, parents can turn it into a kind of game, so that kids can familiarise themselves with planes and flying, and achieve more comfort and control when the moment of truth arrives.
One good example is to bring something fun to draw with (coloured pens, pencils, whatever their favourite medium is – even, these days, an electronic tablet art program), and both before and after takeoff, suggest they draw the airplane they’re traveling in. This provides the double benefit of distracting/entertaining them as well as creating more of a comfort level with the concept of flying. They could even depict themselves piloting the plane! 😉
That way, fear of flying becomes mere child’s play.