There's Always. This is apparently a remake of a movie called A Guy Named Joe. I haven't seen the older movie. The newer one is directed by Spielberg. It's not really about flying, though flying is a major part of the plot.
If anime interests you at all, certain points of Cowboy Bebop lead me to believe the creators have a love of aviation, though aviation isn't really the point of the series. The creators basically just throw "shout-outs" to aviation in their show. The movie has a scene that takes place at an airshow, which is pretty cool. I don't know that you'll dig the whole series just to see a few references to aviation, though.
About all that's left are the myriad WWII re-enactment movies like Tora Tora Tora or Midway. Use of actual aircraft footage is mixed when you watch these movies. Well, Tora Tora Tora was better than average in this regard.
There's The Final Countdown, which is also not solely about aviation. The premise is really cool. There are a few scenes that have plane candy. Bonus points if you can spot the scene where the Tomcat driver nearly crashes his very real F-14. Yes, he was showboating. I bet his commander had a few choice words for him after the shoot.
I almost ended the post without mentioning Strategic Air Command. What do you get when you get a studio who nabs a real Air Force Colonel (or General?), a real squadron of B-36s during the cold war, and a shout out to a man's love of baseball? Yup. This is Strategic Air Command. I haven't seen it all the way through, but I remember thinking I certainly should at some point.
