How can I transcode a FLV video directly to mp3 on CentOS?

Firstly, ffmpeg is the tool of choice for this. It's CPU-intensive because that's the nature of encoding video or audio.

You can simply rip the stream (assuming original mp3 audio is in the stream) from the track and save it. I've used this bash snippet before for directories of *.flv files:

#!/bin/bash
for i in *.flv; 
    do ffmpeg -i "$i" -acodec copy `basename $i .flv`-`date +%H%M%S%N`.mp3; 
done

If the stream is not natively in mp3 format, you need to re-encode. Or perhaps you want a different bitrate, etc. This task will definitely consume more CPU than the former:

ffmpeg -i "$file" -f mp3 -vn -acodec libmp3lame -ab 192 `basename $file .flv`-`date +%H%M%S%N`.mp3; 

edit: to limit to one core: taskset 1 ffmpeg <rest of args> -- taskset is part of the util-linux package on Debian systems. You may also want to renice the process, setting its priority value to something in the positive range (sounds backwards, but lower nice value = more cpu time). As always, man taskset, man renice, man nice.

This is how you do what you want to do with ffmpeg from the shell -- implementing in PHP is left as an exercise for the reader.