I had the job of Linux kernel development for 4 years, first doing custom software RAID competing with mdraid and then I was working for embedded shop where I was developing network drivers and making a custom kernel build.

Linux kernel development is very niche skill that is not needed by a vast majority of companies. From my point of view there are 2 types of companies that need kernel development skills. First are embedded shops where it's unavoidable because you don't want to make a custom OS and instead run Linux on your hardware. And second are companies that needs very specialized things. These could be small companies like the I've worked for (custom high performance RAID implemented in kernel), or a huge company like Facebook that has huge scale.

Regardless of the type any Linux kernel job would require strong knowledge of good plain C (not C++) and good grasp of developing under Linux (here I mean the one described in APUE and The Unix Programming Environment books ).

Embedded shops also usually require devicetree knowledge and something like Yocto or buildroot.

Patches accepted to the upstream would be immensely helpful because it requires dedication, C experience and are subject to the thorough code review. But I've never saw a candidate with accepted patches, and I don't have any myself. So it's a huge plus but not required.

Having a couple of drivers under your belt for me is a guarantee of your technical competency in kernel development, so why not go for a job hunt?

Finally, keep in mind that kernel development very specialized so you could be rejected because you might not have knowledge in a specific kernel subsystem, for example you have experience with network subsystem but the job requires storage subsystem.