In a way it is. Yes, you can animate an arrow along a path in Flash. However, in the After Effects tutorial the tail of the arrow follows the path a well, bending when needed. That is something that is going to be difficult, if not impossible to do in Flash.
You could, however, animate the arrow in After Effects just like in that tutorial, export it so that the background is transparent and then put it into Flash. Not the most elegant method and it might not be practical in some cases, but you could give it a try.