How many flights on average does it take to fly solo?

I've seen people be completely stable on their own in as little as 5 minutes and I've seen people with over an hour of time time still unable to control their movement. The difference is not in natural ability or skill, but rather in ones ability not to move around. It isn't a natural feeling for the human body to be in free-fall, so the natural reaction is to flail your arms and legs about in an attempt to gain stability. Doing this in a wind tunnel has the opposite effect. It gains instability. So the people who learn to fly by themselves quickly are the ones who can stay still while the people who take a long time to fly by themselves are the ones who can't stop themselves from flailing about. It's really that simple: just don't move. Your instructor will make sure that you have the proper body position for you to stay stable in the wind. All you need to do is hold that body position and fight the natural urge to flail your arms and legs about.

Assuming you "catch on" quickly (it's all in the way you position/move your body) your flight instructor will let you free-fly on your first trip.

I got my level 1 flyer status after approximately 33 minutes in the tunnel, split on 8 different visits. But your mileage may vary.