$ convert bw.jpg -format "%[colorspace]" info:
Gray

sudo apt-get install imagemagick

for i in /images/folder ; do
  if [ "$(convert $i -format "%[colorspace]" info:)" == "Gray" ]; then
      mv "$i" /images/folder/bw
  fi
done

$ convert black-and-white-comics.jpg -colorspace HSL -channel g
>         -separate +channel -format "%[fx:mean]" info:
0.00781798

@echo off
setlocal ENABLEDELAYEDEXPANSION
if not exist bw md bw
for %%f in (*.jpg) do (
for /f %%i in ('magick %%f -colorspace HSL -channel g -separate +channel -format "%%[fx:mean]" info:') do set VAR=%%i
if !VAR! LEQ 0.05 move %%f .bw)