No, it's not possible in any generally consistent way. Remember, these flash players are actually
separate programs being loaded and run by the flash plugin, and are designed to fetch the video directly from the hosting server, independently (or at least semi-independently) from the browser or the page itself.
Not that I know anything about the technical details, but while it's obviously possible to snoop out the actual video url for many of them, the technique is different for every player and site. And it may simply be impossible for some of them.
About the only thing you can do usually is to use one of the many online downloader sites to fetch the video for use in your stand-alone player.
This one, for example, supports many sites and even has a firefox extension available.
Perhaps things will be change if and when HTML5 video becomes popular enough to replace all these flash players.
