How do I pass Jump School with a Fear of Heights?

I wouldn't so much worry about the jumping, and falling into nothingness: It's the sudden stop that will kill you!! Best way to prepare is to arrive at Ft. Benning in good shape with a well above average APFT score. Listen to your instructors and take training seriously, but still have fun along the way. You will get a little sick and queasy, but that comes with anything that you do the first time in the Army. That's natural. Channel that nervousness into something useful, like checking and rechecking your gear, and that of those around you. When you stand up, hook up, and shuffle to the door, the adrenaline will push away your fears......move to the door, think about getting a good door position, and then you'll be mercifully sucked out of the plane. Your parachute and gravity will do the rest. Make sure that you check your canopy, and steer clear of other jumpers around you. Enjoy the ride, but concentrate on getting into a good and proper landing position. Ground rush is for real!! Get ready for it. If you are lucky enough to make it to an airborne unit, learn to embrace everything about it. It will get better and you will learn to love it. Airborne, All the Way!!

I was afraid of heights when I went to Airborne School. In fact, I still am. Now I'm a Master rated Jumpmaster.
Looking at the ground from that height is more surreal than anything. It's scarier to be on a high dive than 1000 feet in the air.
As the jumper, you just sit in the plane and distract yourself. Sing a song, sleep, think of anything but how scared you are. It's good to have a ritual. There was a certain song I sang to myself for the first ten jumps or so.
After that, you just have to walk to the door. The JM will help you get out if you stall. I'm not saying I've thrown anyone out.... But I've definitely never had anyone who stalled in my door not make it out lol.
The fear never goes away, but you learn how to overcome it, and that is a skill that you can apply to every fear in your life.

Jumping is different. Height isn't a big deal.

I dont like heights, either, but it is easier for me to jump than climb a ladder.

Just chute up, hook up, and go.