Seems to me you'd need a handle to the root window/desktop, which would have far-reaching effects, since it'd just about have to be global.
Is that a problem? al_set_new_display_flags() controls global state like whether it's fullscreen, windowed, or "frameless" windowed.
You could add a flag there for when the window is generated. But I'm not up-to-date on A5. It looks like that function is a "call once at setup and never again" type. So that would rule out changing the flag at run time, yes? (Though, one could easily leave it on and just not use it.)
al_set_new_display_option(), seems more like the the right place to me ("Display options differ from display flags, and specify some details of the context to be created within the window itself.") but none of the listed options really seem similar to what we'd be setting.
I'll probably spend some time looking at the *NIX / Windows API calls and see if "run-time" switch is even an option on them. If not, that particular problem solves itself.