On Ubuntu 16.04 a USB flash drive is mounted in
/media/$USER/LabelName, but it's possible to handle the file copying without knowing it. A rough script would be:-
while sleep 1
do [ -e /media/$USER/*/TheFile ] || cp TheFile /media/$USER/*/
umount umount /media/$USER/*
xmessage -center -timeout 3 "File copied - change disc"
This is just to show the principle. One thing you need to do is make sure there is nothing mounted in
/media/$USER/ before you start (unless you have already mounted the first drive). You can replace
TheFile by a parameter or a preset environment variable, but make sure it's in your current directory, so that there's no path, otherwise the check for its existence on the drive already will fail.
You can probably do all of this on an Ubuntu Live disc without installing, but you'll need to check where the pen-drives are mounted and modify the script if necessary; also I'm not sure if
xmessage is included on a Live disc, so you may need to install it, unless you use another method of indicating that the drive needs changing.