To answer the actual question… Flash doesn’t have any type of recording feature like that.
The example link you pointed to, I would guess was captured with a program that records your screen, then imported to Flash from there.
Another way to “fake” the effect you’re looking for, is to draw the whole arrow, then animate a mask layer over it that will progressively reveal more and more of the stroke.
I found your post because I am trying to do something similar, except for me, it is important that the brush strokes look like they are fine art, realistic looking AND animated. So far I’ve been fruitless. 🙁
Good luck! Feel free to email me if you have a question.
Reagan