[410] what I need to buy to make this work on my GreenBull machine and the redfly?

Since this 4th axis already comes with a stepper motor, you will need a driver and some cable to connect to the driver from where the 4th axis will be placed. If you have extra space in the redFly electronics enclosure, you can fasten the driver there. You will also need some wire to connect the driver to the breakout baord.