Flash Player is a browser add-on, not an executable player.
There is a standalone player (Projector) that you can download from http://www.adobe.com/support/flashplayer/downloads.html, but this player can only play .swf files.
There used to be an Adobe Media Player to play .flv files, but is is no longer available. Use a 3rd-party player like VLC Media Player to play .flv files.
Thank you, Pat. I did not realize this, so no wonder I have been scratching my head. I appreciate your suggestions, too. :-)