Faster run-up gives your flip more rotation 

The faster you run, the more rotation your flip gets.
It is because some part of rotation is initiated by a friction.
Assume that you run and then you step on a place where a friction is stronger.
What would happen?
Your feet are fixed to the ground just a second by friction but your upper body is still going forward.
This is rotation.

Probably you have an experience that stumbled and rotated forward and scratched your face.
That is the same.
When you punch/jump, more weight are applied to the ground so that friction become stronger and fixes your feet(The heavier, the stronger a friction becomes).
It can be said that a frictional force initiates rotation.
A frictional force works in the direction where the frictional force prevents an object’s motion.
If you move forward, a frictional force works backward.
That frictional force is not applied in the direction of your center of gravity, so it initiates rotation.
(cf. To arch your back makes rotation but decreases height)

How to make a frictional force stronger?
It’s easy.
You should make your motion faster.
To do that, you should make your last jump before flip lower and longer.
All of your speed should be used for horizontal motion.