You have a potentiometer joystick. This means each axis on the joy-stick is a potentiometer (a variable resistive divider). The plus and negative leads power the joystick (it says so in the datasheet so I'm not sure why you asked this). They provide the positive and negative endpoint voltages for the resistive divider. The center line is biased to be exactly half this voltage at all times.
The rest is all down to the AmpFlow controller. Whether or not it will use the center tap is in the user's guide. The center line may or may not be needed depending on what the AmpFlow decides is center: +V/2, or the center line voltage. If it is the former case then the AmpFlow will need some access to the joy stick's voltage (such as the electronics and joystick being powered off the same supply). If center-line is not needed, just leave it unconnected. DO NOT connect it to any end of the voltage supply or it will force your joystick to be stuck in an extreme corner position.
All of this was already answered in one of the other versions of this post. I believe this topic has been triple posted now. NO need for that. I'm getting lost in all the different versions.
Why did your last controller burn out? Didn't you have a fuse? It's dangerous to be using such high currents without a fuse.