Here's what you need to do: by default, Ubuntu comes with only open source software enabled (I think that's the case, anyway). If it's still not working, try a reboot (there might be some bogus reference to the old plugins somewhere). A restart of your browser(s) is required though. Now you will have full 64 bit Flash without any wrappers and other garbage in both Firefox and Chromium. One extra package, 'adobe-flash-properties-gtk' will be installed automatically. Try quiting and restarting Synapic, then click on 'Reload'. If it's not in the list, something went wrong with updating the package lists.
#Install adobe plugin for firefox install
Install the package 'adobe-flashplugin'.Update the package list (don't count on Software Center doing this for you, it sometimes doesn't) by clicking 'Reload' in.