I used for long time the Hobbyking KKboard flight controller for my quadcopter and unfortunately this one is getting old and it’s hard to find ressources about it!
To flash it with new firmware you will need:
An AVR / USB programmer
Download the flasher, and launch it (with administrator rights):
Select the correct board: Hobbyking quadcoper control board and the firmware you want. I personally prefer Quadrocopter v4.7 by Kapteinkuk and press flash button (green icon on the right).
The flasher should start blinking and text appears in console. If everything goes good you should see: “Flashing of firmware was successfull”, else check your wiring or browse faq!
Have fun and good flight!