Are you using the FLVPlayback component to play the video in Flash? and you have given that a "skin"?
Are you then Publishing an HTML Web page with should have the Flash on it but doesn't?
A pathing error comes about when the FLVPlayback component (the .swf), can't find the .flv file.... so of course the video doesn't play.
This often happens when subfolders are used to store either the .swf and/or the .flv file in a different folder than the HTML Web page.
The trick to using subfolders is to remember that once the .swf (the video player) is placed on a Web page, you are in effect moving the .swf to the same folder as the Web page and hence must have the path to the .flv file relative to that Web page, NOT the physical location of the .swf.
So let's say you have your main Web site root folder and one sub folder called "Flash"... inside that is the .swf and the .flv.
If you create a path inside the .swf diectly to the .flv ....."contentPath" = "my_video.flv" it will play just fine when testing directly in Flash....which is NOT a good sign.
Then if you take that same .swf and code it in on a Web page that is outside that "Flash" subfolder.... the .swf is still expecting the .flv to be in the same folder that the .swf is in... not some subfolder...
But in reality, the path from the Web page to the .flv now become "Flash/my_video.flv.
You can edit the path by clicking on the FLVPlayback component and then down in the "Parameters" panel edit "contentPath" and path it relative to the Web page, NOT the actual location of the .swf.
And note, once correctly pathed relative to the Web page, testing the .swf directly in Flash.... will NOT display the video, since the .swf is now pathed to work on the Web page, not as a stand alone .swf.
Hope this helps clear up any "pathing" issues you may have.