Front handsprings -
If you have the time, learn front limbers. It helps with that feeling of moving forward and letting your feet blindly hit the floor.
I teach front handsprings by taking a porta pit (2-3 stacked 8 inch mats) and having gymnasts do handsprings onto their backs. When they can show a solid reflection from the floor (by coming in short on the handstand and blocking through their shoulders, looking at their hands as they come over), I hand spot them onto 2 stacked 8 inch mats to their feet.
When they can do the handspot relatively easily, I remove an 8 incher and have them do a front handspring on their own into 1 8 inch mat. Then when comfortabel, move to a sting mat, then floor.
The hard part is learning to not go through the handstand until past vertical with the shoulders.. I know that sounds awefully wierd, but if you think about it, it's just like a handspring on vault, only you drive your heels while you block instead of on the rise.
If you are thinking of flyspring drills, I start with bear walks. You can use that body position to show your gymnast how far their punch should travel.
Then, I take an 8 inch mat, and do punch to handstands, and drop. When this is done easily, put a folded pannel mat where their hands should hit from a good punch, and handspot the flyspring, telling them to drive their heels when they hit the handstand. When they can do it on their own, have them simply unfold the mat bit by bit until it is floor level. Then they have a flyspring.