How can I dodge missiles while playing a fighter-jet match?

I've done this in both online and offline and have a 90-95% success rate...

As soon as you hear the missile lock alarm, you want to perform a roll-off-the-top. As soon as the alarm sounds, pull back hard on the stick at full throttle to start your loop. The moment you are at the top of your loop, roll over so your fighter is level with the ground again.

When successful, you should see the missile pass high to your left or right and you have also broken visual contact with the other combatant.

Note - If you are just leaving the military base with the jet, especially online, after completing the roll-off-the-top you want to immediately drop your altitude to as close to the ground as possible, ideally over the ocean. This will prevent the base from getting another missile lock on you.

All of these answers are nice, but now you're talking to someone who trains pilots on GTA 5. :p

The off the top response was good, but what you will want to do, is get as much altitude as you can before hearing the lock on. The moment you hear this, you will motion your plane at a hard downwards angle; But pulling to the left or right. By this time, you will have oriented your jet to normal flying and have a clear target on your enemy.

I've watched a lot of people try the pull up to the side trick; And about 8-10 of them had been shot down by me; Here's why. I see them pulling up to curve, and I will instantly pull up as well and aim my actual cannons in front of them just a bit. By the time they are fully turned around like the above post, I already started firing at the nose of the plane and letting the pilot fly into the burst of explosive rounds. The earliest I've caught someone was they were in mid turn and I've caught them right in the center mass of the plane.