not many, I did it, jobs are scarce, most of the time you port a new version of CPU to the kernel, or add a few device drivers, the industry does not need a lot of those engineers, and per my experience, not compensated that well either. these days many kernel programmers work for big companies.
I remember Apple having a lot of related listings so I'd assume companies that are somehow involved in OS development (Microsoft, Google, maybe RedHat/IBM and Intel).
Significant portion of kernel code is written by FAANG, for example. There are other companies that also pay reasonably well. You can check some statistics of contributions to Linux kernel here https://lwn.net/Articles/909625/
Defense industry has a few such jobs, working a lot with RTOS's, network devices, sometimes even embedded for signal processing/control systems, etc... The big defense contractors probably pay better than working directly for the govt depending on where you live.
