[blimey]

I would use concatenate feature of (the newest version of) ffmpeg.

Use the files in their original flv container if possible.

Create a text file "mylist.txt" with all the files you want to have concatenated in the following form ( Lines starting with a dash are ignored ) :

mylist.txt:

# this is a comment
file '1000.000.flv'
file '1000.001.flv'
file '1000.002.flv'

Note that these can be either relative or absolute paths.

Copy the mylist.txt file into the same directory with ffmpeg and all of the files to be concatenated.

ffmpeg -f concat -i mylist.txt -c copy concatenated_output.flv

Then you can just mux the video with the audio.

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Edit:
I left out a step that I had forgotten about that applies to be-at.tv flv videos only.
Before concatenating, run each flv through ffmpeg in order to strip the timecodes (so that each video starts at 00:00, rather than an 01:01, or 02:01, etc.)

For example:

ffmpeg -i "1000.002.flv" -vcodec copy -acodec copy "002.flv"

Do this for all the original flv files, and then concatenate the output files only by putting the filenames in the mylist.txt file.