To fix the problem of Duke always moving to the right even with a calibrated stick, open NUKEM1.conf in the SteamApps/common/Duke Nukem 1 folder and find the line "timed=true" and set this to "timed=false"

This should give you perfect control over Duke with a gamepad. Note that you can also press ctrl+F1 while DOSBox is running the game to bring up the mapper and bind things like the Enter key to a button on your gamepad/joystick to easily close dialog boxes without touching the keyboard!

I hope this helps my fellow Duke fans and I would appreciate it if someone from Interceptor/3D Realms could consider patching the .conf file in the future to at least have timed intervals for joysticks set to "false" by default.