In Unity you should have a Gtk menu. Everywhere else you should have the Opera button menu. What does it say under the System section of opera:/about.
Could I also have a screenshot?
P.S. You can force the Opera button menu by starting Opera with --show-opera-menu but you would need to edit your .desktop file to make this permanent.
You don't need to have Chrome installed. If your distro supplies a Pepper Flash package we can use that instead. Debian and Ubuntu do and users of those distros can just install this. If your distro does offer a Pepper Flash package but Opera is not seeing it, please comment in this thread.