I read both sites.
The joystick spec seems clear. The positive and negative leads go to +12 Volt (if you have the 12 Volt unit) and gnd respectively. This is to power the joystick electronics. You can use the "12V output supply for controller electronics" from the ampflow unit. BUT, I would measure it before connecting it to the joystick since the ampflow spec does not say that it is regulated. It may be 16 Volt or more and therefore needs an external regulator to ensure the that joystick receives the correct voltage, ie. either 10 Volt or 12 Volt.
The output voltage is specified as being with respect to the centre tap. So you will need a differential amplifier to convert this signal to a 0 to 5 Volt signal that is necessary (see below) to control the ampflow.
So I suggest that you experiment with the joystick, connect a voltmeter between the centre tap and the output and measure & record the voltage for various joystick positions.
I found the ampflow info short on detail.
However, I believe that you need the "Analog input" which requires a control voltage in the 0 to 5 Volt range. So if I were you, I would start by connecting a potentiometer of say 10 k Ohm across the 5 Volt source provided by the ampflow unit with the pot slider connected to the ampflow input. You will need a motor connected to the output of the ampflow. Connect a voltmeter between gnd and the pot slider and record what the motor does at various voltages.
When you have this info, we should be able to advise you further.