You can get a Firefox addon called,
Live HTTP Headers
1. Install the addon
2. Restart Firefox to activate the addon
3. Open the addon
4. Visit the webpage that contains the video
Also, another solution is to download the Maxthon web browser, which has an option to save files/elements directly off a web page simply by hovering your mouse over the target image, video, etc then clicking the " + " sign that appears. You can do a save-as and that's it or you can use the file sniffer to get the direct path of the *.FLV video or even *.SWF for that matter.
Some *.SWF videos get a bit trickier, but *.FLVs are very easy to download. These methods might seem complicated but they are really not. A lot of the addons for Firefox should work in downloading *.FLV videos, but they don't work (as I have found) for *.SWF videos. More people will eventually move to *.SWF videos because its easier to secure the video preventing less downloads of content they don't want shared. It's not impossible, just a bit more difficult for some people.