You don't need to do anything to start flying planes. You can steal it as one of the first things you do.
Here's what you do:
Go to the airport and jack a really tall vehicle. Park it right next to the fence. Jack a regular vehicle and park it next to the large one. Use it like steps to get over the fence. There is a private jet and a dodo there. Fly safely, the planes assplode much easier than they used to.
Right now I'm a little pissed at the game. I used a map to find all the gang tags so I could get the weapon spawns at CJ's house. Well I went to all 100 of them and now I only have 99 tags. I think what happened was I stopped spraying before I got credit for one of them or accidentally marked one as done when it wasn't done yet. Now I have to go back to each one and find out which one can still be targeted.