How to feed custom RGB Led keyboard backlight
Your very best bet is to use Neopixel LEDs and a small Arduino as a controller. These are designed to be individually addressable, easy to wire together in a daisy-chain fashion and there are lots of examples of controlling them with Arduinos.  

Adafruit is a great place to start: https://learn.adafruit.com/adafruit-neopixel-uberguide