Kernel 3.16+

Has anyone tried to compile one? Would be great if some experienced members could give instructions.

You can run the latest upstream kernel but with that you need open source versions of the user space libraries as well and they have many limitations. E.g. no video acceleration, OpenGL is quite experimental, no accelerated X.Org support with 3D, etc.

If you need proper HW acceleration and power management, you need to use the officially supported 3.10.x version.