This is THE reason I come back to play GTA3, it's just so much fun. My record is 30 minutes, upon which I became extremely bored and landed. I have to say I've gotten pretty good handling it, and can do barrel rolls no problem.
How to Fly
First, get into a plane and head to a runway. Hold the accelerator, down, and side view. Wait until the plane begins to spark underneath, then return to normal view and let go of down. The plane will immediately begin to fly up. Now, tap down whenever the nose of the plane (red part) is visible. You only want to see the white wings of the plane. Remember, NEVER press up. If your plane begins to go down, don't worry, it'll eventually start to come back up. To turn, gently tap left or right, and always remember not to see the red nose of the plane.
To do a barrel roll (plane spins all the way upside and over, then returns to normal position), first gain some height by flying for a bit. Then, force it down by holding down until it's fairly low. Let go of down, and let it really start to gain speed as it's going back up. While it's going back up, hold left or right and it'll begin the spin. Once the spin is three quarters done, hold the opposite direction so that the plane levels out and flies straight, otherwise it'll continue to spin.