I am designing a board with 9 SK6812 LEDs. On the back of the board I want to place the Atmega328P microcontroller.
I have doubts whether the heating of the LED can affect the operation of the microcontroller?
Board Thickness: 1.6mm Two layers
The data sheet of the SK6812 that I was able to find made no mention of the amount of current required to the device when the three LED are lit. As such it is not possible to directly calculate the net power consumption of nine (9) of these devices on your circuit board. You may have to setup an experiment to measure the current draw of one of the SK6812's using a breakout board that includes a chip of that type.
Once you know the worst case current draw of a SK6812 with all three LEDs lit (propose that the RGB color would be "white") you can proceed to compute the total power of your LEDs. Only then can you start to consider whether the MCU on the back side of the board would be exposed to excessive temperatures.