I run a NUC6i3SYK (Skylake Core i3-6100U)
elementary OS Freya (Ubuntu 14.04.)
After trying several other Kernels I now successfully run the 4.2.8 Kernel.
Below kernel 4.x (3.19 is now the stock Freya/ Ubuntu 14.04 Kernel I think) I don't have Wifi and I see quite the CPU load even in idle.
On kernels 4.3.x - 4.5 I do have Wifi but terrible ripping graphics glitches and interruptions.
Kernel 4.2.8 runs perfectly fine for me, including WiFi and smooth graphics, While typing this on Firefox I have a CPU load of 1-2% and a 34°C cpu temp.
Please note: To get hardware graphics acceleration you need to add "i915.preliminary_hw_support=1" to Grub kernel parameters.
Easiest way to do is with Grub Customizer. My kernel parameters are now:"i915.preliminary_hw_support=1 quiet splash".
Then save in Grub Customizer and to make sure it is really really saved you should finish with "sudo update-grub" in terminal and reboot.
So yes, in my case Freya with Kernel 4.2.8 "supports" a Skylake CPU (6100U) perfectly fine.