Well, the first flip in the video used a take-off like that of a double-leg (90 degree bend at the waist, flip sideways), which is a bit harder to get vertical height with.
The second flip looked like it used the sideflip jump, which can best be described as the same jump for a backflip, sideways.
Haha,
http://www.youtube.com/watch?v=E2aS39c331s shows this better than I can in words, the "push arms up at moment of jump" pause is what I'm referring to.
If you watch a lot of videos, not everyone throws their arms up fully, it's completely feasible to use only your legs to jump; this just doesn't fully use all the up-force you could generate.
Now to keep you from landing facing where you came from, just watch a point in front of your body while you flip. The BEST exercise of this (and an all-around cool experience) is to watch yourself in a mirror as you sideflip. Now I'm guessing you don't go to a local gym, so this may not be viable, but the idea of watching yourself flip in a mirror should help get across what I mean.
