The stock email client and silk browser both include buttons placed on the menubar/toolbar at the bottom of the app. I would like to place buttons there in my own application but after having searched around I have been unable to find a way to access the menubar to place ui components there.
No, this is not possible. The bottom menubar is the Fire's way of implementing Android hardware buttons. As such, the team did not expect or want people to modify that component.
The only option you have is to add context menu items, which will show up when the context menu button is clicked.