# For MP4
ffprobe -v quiet -select_streams v:0 -show_entries stream=bit_rate -of default=noprint_wrappers=1:nokey=1 a.mp4
 
# For MKV
ffprobe -v quiet -select_streams v:0 -show_entries format=bit_rate -of default=noprint_wrappers=1:nokey=1 a.mkv

returns:

4717811

ffprobe -v quiet -select_streams v -show_entries packet=size -of compact=p=0:nk=1 input.mp4 | awk '{s+=$1} END {print s}'
1772586389
 
ffprobe -v quiet -select_streams v -show_entries stream=duration -of compact=p=0:nk=1 video.mp4  # format=duration if MKV
3592.544000
 
echo 1772586389/3592.544000 | bc   # B/s
493407
 
echo '1772586389/3592.544000/1024' | bc   # kB/s
481