Hi Sylvia, Welcome to Indy Gear.
What you are doing in your video is more of a modified cattlemen’s/gypsy style crack then a flick. You set it up a bit differently (like the flick) but the whip is still forming a top-rolling loop early in the throw then continuing straight out over length to produce the crack. Your developing a great rolling loop (Similar to a technique Anthony DeLongis is known for) that produces a very smooth and precise crack, and works well for targeting but is different from the flick.
The flick, (overhand, underhand or sidearm) basically forms when you cast the whip out in a similar motion to throwing a ball. Rather then the whip forming a rolling “loop” though, It develops a hairpin curvature or U shaped bend as it travels out. Like the rolling loop, this motion intensifies the momentum of the whip as it curls along on itself allowing the energy to becomes more focused; producing the crack.
Flicks can be a tricky to master. Adam does a good job of explaining it in his youtube video
http://www.youtube.com/watch?v=Od7JBEIQj7M
but it's not uncommon for someone just learning to struggle with it a bit, especially with out having someone next to you, to walk you through it step by step as you practice. With any type of flick though, timing is especially important. The technique itself is relatively simple, you are dragging the whip from behind, then pushing it forward when it's at your side. Finally pulling the handle forward as it moves out in front of you, giving it extra bit of force to form the hairpin and make the crack. But it takes a little time and practice to really develop the technique and get the feel for where to speed up and when to let the whip follow through.
Keep at it.
Dan
Now I know what the difference is... 
I mean, I called "flick" two different things.