AVI (at least with the codec DV AVI type 2 with 48khz sound) is an edit file... FLV is an output file not designed to be edited
As the others say, in order to play an FLV file, you must have a Flash player on your computer.
Most web sites that use FLVs on their sites (i.e., YouTube) have Flash players built right into their sites.
FLV is a streaming, delivery-only format, and is not meant to be editing - only played.
Now, Moyea has some utilities to edit them and convert them, but still, they are not intended for editing. I use their FLV-Importer for Premiere plug-in, when I just have to edit that format. It works fine in PrPro 2.0 through CS3, but will not work in CS4 PrPro. However, as of CS4.2, one can Import FLV's. I just do not know how well, or if at all, it works with PrE, as I have never tried it.