Firstly, you must have finished the War Machine levels to unlock the parachute.
Load up mission 8-2 from the DNA menu (Pause > DNA > Sequence 8 > Memory 2: An Apple a Day). Climb up the wall in front of you, and then the wall to your left. Then climb to the top of the big post. Now face the bridge, jump off and press Square to deploy your parachute.
It is not possible to do this during the first run of the mission as they take your parachutes away. It only works when replaying it. You could do this outside of the mission, but using the mission allows you to skip most of the climbing.
I used the following video for reference: