In case anyone else has the same issue I had where the game is trying to calibrate your joystick and is not recognizing any of your button presses, try this.

Go into your dosboxWC3.cfg and change buttonwrap=true to buttonwrap=false

So happy I can play with something besides mouse+keyboard now!

Top Tip.

I have a Thrustmaster joystick and am using JoyToKey to do the mapping but found that all my buttons were either button 1 or button 2 in the game. So pressing the button that I'd mapped to the afterburner would roll the fighter when I also moved the joystick as it was being picked up as button 2 even though it is button 9.

Changing this setting stopped my other buttons being picked up as either button 1 or button 2.

Thanks :)

If after this change some inputs are still not recognised correctly you can use the DOSBox Mapper (Ctrl+F1 in-game) to assign the equivalent mouse or keyboard inputs to the affected buttons.