If I am trying to grab data off an unknown site, I usually use either SmSniff:

http://www.nirsoft.net/utils/smsniff.html (standalone)
or
http://livehttpheaders.mozdev.org/ (Firefox plugin)

Sometimes the FLV video is streamed from a server rather than being downloaded as an FLV over HTTP, I haven't looked into that sort of thing too much, I think it would need special capture software rather than tinkering with a browser/download manager and UserAgent headers.