Inductive kickback when applying PWM to the output of an alternator
You won't have inductive "kickback". This occurs when you suddenly disconnect an inductive load. This is not going to happen in your case.

The three-phase supply from the alternator will be reasonably good DC without any stabilisation.



Figure 1. Rectified three-phase alternator output.

Your schematic shows the micro-controller driving an NPN transistor in emitter follower configuration. The most you can get out of this is the GPIO output voltage (probably 5 V) - 0.7 V drop across the base-emitter junction of the transistor giving you 4.3 V on your LEDs. This is probably not what you want.



Figure 2. An NPN transistor can be used to act as a switch controlled by a low-voltage micro-controller switching a high voltage or high-current load. Source.

The linked article explains how to calculate resistor values.