This is probably the best article that explains in details the calculations behind making a motion-blur in the direction your object is going.
http://labs.byhook.com/2010/02/11/simulated-motion-blur-in-flash/
It covers Linear, Curve, and Directional motion blur. Linear and Curve in this article don't necessarly "blur" but instead "trails" the sprite along the previous and current path.
Directional blur looks the most pleasant, although the sharp turns of your sprite may have a noticeable blurred angle.
Some developers claim to achieve this motion blur by simply modifying a BlurFilter's blurX and blurY values, which is fine with horizonal / vertical movement (respectively). But anything in diagonals, this will look quite a bit off as it will just result a Gaussian blur (at 45degrees, basically it would have equal values in blurX and blurY, no sense of direction).
Another way this might possibly be achieved is with a Shader. This would require some knowledge of PixelBender - you would then create a filter that can take the source image, an angle and an amount parameter (so you can make longer dramatic blurs depending on the distance you move). You would then feed this information to your Shader filter and that should achieve the same result (maybe even faster than strictly doing it only in AS3).
The new Flash Player has some 3D capabilities and hardware acceleration, so it might be worth checking if this filter is already available or created by someone else! :)