Sure, you can fork the kernel, but good luck with that!
The only barrier to forking is the fact that most kernel developers are not bothered by Linus. Which raises the question of why we should want a fork if nobody wants a fork...
The other barrier is the effort required to compete with what is currently the most used Linux kernel base. It's not like forking OpenOffice, KDevelop, or Eclipse where you can compete as an alternative on top of a standard OS. It's replacing the basis of the OS that everything else is written to work for.
The problems with forking are social. You are only going to have a handful of people working with you instead of Linus (because nobody cares that Linus can be a meanie) and as a consequence you are only going to have a handful of people using your fork instead of Linus' (because nobody cares that Linus can be a meanie). Because of this progress on Linux will progress faster than progress on your fork, which will make your fork obsolete (but nobody would care, because nobody would be using it, because nobody cares that Linus is a meanie).
These are not problems with forking Linux. These are problems with forking anything if nobody cares about your fork.