Hello,
Unfortunatelly in most cases using flat review is the only
way on how to navigate and activate Firefox toolbar buttons.
Default Firefox functionality do also have other means on
how to activate themsuch as bookmarks menu, View and Sidebar.
When firefox displays an alert at the top of the screen
such as when installing an addon, when subnitting a form and
similar it is possible to find out a button that places focus
to the alert at the top by tabbing past the address bar i.e.
I do usually press alt+d to jump to the address bar and then
press the tab key to find context sensitive button or the
button that opens Page info dialog.
Another not very obvious place that is accessible and
plugin authors tend to put their items is web content popup
menu. I navigate the web like normal using quick nav keys or
arrow keys, make sure no link or other focusable control is
selected, press the applications key and explore the menu.
Yet another place where there might be some hidden menu
entries is the selected tab popup menu. If you do have
multiple tabs open in your Firefox window just press ctrl+d to
jump to the address bar and keep pressing the tab key until
the tab gains the focus. Here you can activate a popup menu
by pressing applications key on the right hand side of the
keyboard.
For example this has a mute tab menu item inside that might
be usefull if you would like to mute audio on otherwise poorly
designed site.
Unfortunatelly as I have said at the begining I don't know
my-self how to activate the toolbar items other than using
flat review and simulating clicks on them.
Ah yes one more time, for bookmarklets, they can be
activated via the Bookmarks submenu on the menu bar (F10).
And in older versions of Firefox (before Firefox 57).
Plugin authors were also putting their icons to the Firefox
statusbar. This is not accessible as well.
Greetings
Peter