Example:

ffmpeg -s 1280x720 -f rawvideo -i /dev/zero -ar 48000 -ac 2 -f s16le -i \
/dev/zero -c copy -f nut pipe:1 | ffmpeg -y -i pipe:0 -c copy -f nut /dev/null

I see no reason why anyone would do this. Also, there are very few reasons to pipe from ffmpeg to ffmpeg when you can most likely just use one ffmpeg process to do whatever you want.
What the options do:

-s 1280x720 -f rawvideo – Options to describe the input since /dev/zero is not a typical input format and therefore these additional options are required.

-i /dev/zero – The video input. It is being used in this example to generate a video stream out of "nothing". This was used in the example because the question asker refused to provide any information about the inputs being used.

-ar 48000 -ac 2 -f s16le – Options to describe the input since /dev/zero is not a typical audio format.

-i /dev/zero – The audio input. It is being used in this example to generate an audio stream out of "nothing".

-c copy – Stream copy, or re-mux, the inputs to the output. No re-encoding is being performed so the process is lossless. It is unknown if stream copying is acceptable to the question asker or not. Maybe re-encoding is desired instead?

-f nut – You need to tell ffmpeg what format to use for the pipe. Nut is a container format. See ffmpeg -formats for a complete list. Another flexible format is -f matroska, but it is impossible to suggest an appropriate or specific output container format to use without more info from the question asker.

pipe:1 – Use the pipe protocol to output to stdout. Alternatively, the number can be omitted (just pipe:) and by default the stdout file descriptor will be used for writing and stdin will be used for reading.

I would use pcm instead of flac in the pipe, because it takes far less time to process (PCM is raw audio, FLAC takes lots of time to encode).

Anyway, here's how I would do it.

ffmpeg -i <input video file/stream> -vcodec rawvideo -acodec pcm_s16le pipe:1 | ffmpeg -f rawvideo -i - -vcodec <video output codec> -acodec <audio output codec> -vb <video bitrate if applicable> -ab <audio bitrate if applicable> <final-output-filename>

This worked for me when I last tried, but my goal was to pipe ffmpeg into ffplay, which is a slightly different process.

example:

This pipes a video from ffmpeg to another instance as raw video output and 16 bit little-endian PCM (both lossless unless you have 24 bit PCM, then substitute pcm_s24le.) It then converts them to h.264 in the second instance, with the fraunhoefer AAC library from the Android project (libfaac is more commonly included in ffmpeg builds. You can replace it with this instead.)

ffmpeg -i montypythonsflyingcircus-s1e1.avi -vcodec rawvideo -acodec pcm_s16le pipe:1 | ffmpeg -i - -vcodec libx264 -acodec libfdk_aac -vb 1200k -ab 96k mpfc-s1e01-output.mkv

If this doesn't pipe the subtitles, you can always rip them to SRT's and then mux them back in later, or add them to the pipes above easily.

Filters need decoded frames, so the encoded output can't be used directly. You can pipe it to another ffmpeg process.

ffmpeg -i input.mp4 -map 0:v -map 0:v -map 0:v -c:v libx264 -b:v:0 10000k -b:v:1 5000k -b:v:2 2000k -f nut - | ffmpeg -i input.mp4 -f nut -i -filter_complex "[1:v:0][0:v]psnr;[1:v:1][0:v]psnr;[1:v:2][0:v]psnr" -f null -

To avoid decoding the video twice, use

ffmpeg -i input.mp4 -map 0:v -map 0:v -map 0:v -map 0:v -c:v libx264 -c:v:3 rawvideo -b:v:0 10000k -b:v:1 5000k -b:v:2 2000k -f nut - | ffmpeg -f nut -i -filter_complex "[1:v:0][1:v:3]psnr;[1:v:1][1:v:3]psnr;[1:v:2][1:v:3]psnr" -f null -