Let me make the following assumptions for example purposes:
/dev/sdb1 is the partition for the flash drive
ext4 is used as the filesystem
flash drive mounted as /mnt/games
First we add the device to be mounted at boot (ignore filesystem checking, you can make this 0 2 if preferred for filesystem checking)
sudo echo "$(blkid /dev/sdb1 | cut -d' ' -f2) /mnt/usb ext4 defaults 0 0" >> /etc/fstab
Next we mv all the existing ROM data to the flash drive
mv /home/pi/RetroPie/roms /mnt/usb/roms
Create a symlink from the existing location to new
ln -s /mnt/usb/roms /home/pi/RetroPie/roms
Then all should be well.