.FLV is a Flash video. Kinda' videos you get off YouTube etc. If I want to make a small loop out of those things, I import them into Macromedia Flash (or Adobe Flash if you're using the new version) and export it as an image sequence in .PNG format. To make the next step easier, I then isolate the portion of the images I want to make into a loop (eg: image0050.png -> image0070.png)
I then start Adobe ImageReady, import the images as an image sequence, do a bit of cropping, fiddle with the size and the optimization settings then export it as a .GIF.
Only problem here is, this is all assuming you have Flash and ImageReady installed on your computer.