FLVs are "streamed" like a normal file. However you will need a server that supports seeking if you want users to be able to click, say in the middle of the player and not have to load the entire thing (lighttpd has mod_flv which can do this).
You can upload an FLV to virtually any server and use something like flowplayer to play the file.
As for the URL thing, the player just takes in the URL for the FLV to download it. If you know the location of the file then they can easily set up another player virtually anywhere.