If you are using a graphical login manager, such as GDM, it normally will allow you to select your session.
If you want to control sessions through .xinitrc, you commonly need to disable to graphical display manager.
That's what I did on my Debian box. Here's my .xinitrc:
# gkrellm &
# /home/frankbell/scripts/wallpaper.sh &
# exec fvwm-themes-start
# exec fvwm-crystal
Not that "fluxbox" did not work. I went to the Fluxbox site and learned that I needed to use "startfluxbox." The rest of Fluxbox's startup is handled by Fluxbox's own ~/.fluxbox/startup and ~/.fluxbox/init files. (All the other lines are there to start FVWM, which I played with for a few months out of curiosity.)
My Debian .xinitrc file is much simpler than Slackware's .xinitrc, I think because Slackware's must be prepared to understand choices made with Slackware's xwmconfig script.
The Arch wiki
, always a great reference, has a good article on .xinitrc.