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.

hey dude i had the SAME problems you have! i also put the chest high thing up and rolled off of it.. that actually helped me out ALOT!.. got me to get the motion of the sideflip down.. then i just couldnt get myself to do the motion.. i made ONE ujustment!.. i was not using my arms.. maybe that will help.. i learned to throw my right hand ( i do a sideflip to my right ) almost Strait up to get me hight... then throw your front are (to tuck) torwards the bottom of your foot.. just tuck to your shins though.. hopfully that helps