The best way is probably going to be to just parse your webserver's log and look for when Flash requests the video stream (nightly cron job). I'm guessing you are using a pre-existing Flash video player, where you may not have the ability to modify the Flash to push a server request to update the view count when PLAY is clicked, nor do I recommend it because you might switch to another player or to HTML5 streaming.
As already suggest I also agree, just add a "view_count" to your "video" table and increment it, you can do it in one step with (no need to retrieve, add and update)
UPDATE video SET view_count = view_count + 1
Also keep in mind, if you incrimenting your video count upon loading the video page, make sure to exclude page views from search bots (ex: google) because half or more of your view counts could end up being search bots. You can find a list of search bot browser strings, so you know what to look for here.