To help troubleshoot we'll need the following system information:
When reporting issues with video or audio, it's also helpful to get your system hardware and driver details. Instructions for finding this information can be found here:
Finally, sometimes video and audio problems are caused at a lower level and not directly related to Flash Player. I recommend trying both of the links below to see how they perform. If the problem exists with both, then Flash Player is most likely not the culprit as the HTML5 video link does not use Flash Player when playing. You can verify the user of HTML5 by right clicking the HTML5 video and looking for the words "About HTML5" at the bottom of the context menu.
Assuming you are using Windows, please try installing *both* versions of the player listed here: