First create magnitude and phase videos from audio, assuming audio is stereo with 44100 sample rate, then resynthesize videos back to audio with spectrumsynth:

ffmpeg -i input.flac -lavfi showspectrum=mode=separate:scale=log:overlap=0.875:color=channel:slide=fullframe:data=magnitude -an -c:v rawvideo magnitude.nut
ffmpeg -i input.flac -lavfi showspectrum=mode=separate:scale=lin:overlap=0.875:color=channel:slide=fullframe:data=phase -an -c:v rawvideo phase.nut
ffmpeg -i magnitude.nut -i phase.nut -lavfi spectrumsynth=channels=2:sample_rate=44100:win_func=hann:overlap=0.875:slide=fullframe output.flac