Step up and grasp bar with overhand wide grip. Flex knees with hips straight (heels to but).
Kick legs forward and swing upward behind bar. Quickly straighten hips, pull chest toward bar. As chest approaches bar, shift body's direction downward and forward under bar by continuing to kick feet back while hyperextending spine. Allow face to clear under bar, knees to flex behind, and arms to extend fully. Repeat.
Unlike Kipping Pull-up, forward leg kick is not as high, rear kick is directed more upward, and chin does not go over bar, allowing for clearance of face traveling behind and under bar.
To avoid wear on bare hands from sudden shifting movements, use adequate chalk and/or grasp bar with fingers instead of palms and fingers. This technique will obviously require greater grip endurance.
The Butterfly Pull-up is competitive style Kipping Pull-up performed in Crossfit games. It's inception was reportedly accidental, a product of a particular Crossfit competitor being unable to figure out the accepted Kipping Pull-up technique. It's induction into Crossfit games was controversial, but later gained acceptance.
Try the more conventional Kipping Pull-up.
Attempt to perfect movement, making it more efficient by decreasing forward kick (less than demonstrated) while continuing to drive movement with hips.