My goal is to use wget to download an flv file, and pipe the output to ffmpeg to convert it to an MP3. This way the user can download the MP3 without waiting for the FLV to
Part of the problem you're going to encounter is that some file formats have important file container information at the end of the file. Thus, piping a wget call directly to ffmpeg is a potential file breaker as ffmpeg may choke before the file is fully downloaded.
You're better off looking at a series of commands: wget'ing the file then running ffmpeg on it. It ignores the pipe capabilities, but that's the problem you get working with certain files.
Also, I would take a look at this FAQ answer from FFMPEG's site regarding one set of methods when piping videos using mkfifo and concatenating FLV's: http://www.ffmpeg.org/faq.html#TOC27