Fluxbox is a window manager within your X Windows system. You can install fluxbox and not install gnome, but you will be unable to execute any gnome apps you use, like say, Galeon.
But not install X and still have flux, probably not without a helluva lot of tweaking and even then I doubt it since it requires an X server to run
All these "gui"s that you see, gnome, fluxbox, kde they are just faces over the top of raw X. To see raw X type:
instead of startx at a prompt (assuming you haven't started an X session yet). Even then there are bound to be some default settings from your distro, but that's about as bare as you can get easily. The next step is to use twm as your window manager (instead of fluxbox) it's just about the most basic "usable" window manager there is.
Basically what I am saying is that you need X to run X apps (aka gui, with few exceptions such as ncurses). X apps would include the window managers. Fluxbox being just that, a window manager.
X has a client/server framework type setup. Take that for what it's worth, but basically it means that X is your "heart" and whatever you run on it are auxillary or secondary to the heart. Hope that makes sense.