Hi flipandfly,
As a gymnast I have been through it all, including this fear.
A lot of people are saying that you should get spot, and don't get me wrong... great thinking, but eventually you will need to do them on your own.
So first of all, you didn't really give me much about why you are afraid.. I am going to assume it could be the fear of landing wrong, or hitting toes on bar.
1. Keep your shoulders open. Closing your shoulders can cause you to get close to the bar, and if you keep your arms by your ears, there is no way you can hit the bar!

2. Look for your toes. Basically, look for a spot on the wall, and when your toes hit that spot, let go. Keep this consistent, and eventually your muscles will just know when to let go.
One more method I have... this method is actually to help you mentally.

Gymnastics can be tough, and is hard mentally. Think of your flyaway this way..
There is a brick wall, that represents your fear. Right now your wall is stacked all the way up. Every time you go for a flyaway, you knock one brick down. If you balk, (don't let go / refuse to throw) you build up another brick. Eventually you won't be afraid of flyaway, as long as you break down that wall.
You aren't alone on this fear, and remembering that other people go through mental blocks / fears helps me remember to stay strong.
Go for the gold! Best of luck.