.flv is the Flash Video format used to publish videos on websites. The .flv files are normally played by flash .swf player files who load the .flv files.
 How to make one
ffmpeg is a great tool which allows you to make .flv files from most video files. It's real simple (when you know):
ffmpeg -i videofile.avi flashvideofile.flv
It takes only a few seconds if the video file is a couple of megabytes.
You can just wget the .flv file in question. There is also youtube-dl - which is made specifically to download .flv files from YouTube.