Add a timestamp to a video file?
You can use FFmpeg, a free command-line tool, to do this.

Basic command is

ffmpeg -i input.mp4 -vf "drawtext=fontfile=font.ttf:
                        fontsize=45:fontcolor=white:
                        box=1:boxcolor=black@0.4:
                        text='Time\: %{pts\:gmtime\:1466507118}'" output.mp4


(this should be in one line)

The value you need to change is 1466507118. This is the Unix epoch time representation of your intended date and time.