When you install it for the first time, it will download the plugin from adobe, extract it, move it amd symlink it properly for all browsers to see it.
So, if it is already installed, it should have already done all the above. Just to make sure run
# update-flashplugin-nonfree --status
Flash Player version installed on this system : 126.96.36.1991
Flash Player version available on upstream site: 188.8.131.521
flash-mozilla.so - auto mode
link currently points to /usr/lib/flashplugin-nonfree/libflashplayer.so
/usr/lib/flashplugin-nonfree/libflashplayer.so - priority 50
Current 'best' version is '/usr/lib/flashplugin-nonfree/libflashplayer.so'.
and if the installed version is older that the upstream one run
to update it.