I think the best approach is likely to be to set up a GitHub account, volunteer some time on a couple of strategic open source projects, and then leverage that into some remote contract work.
C covers an enormous range of possible applications. It would likely be easiest to work in an area that he's already familiar with. If he's done kernel work, there's always plenty can be done on Linux, but also other systems like FreeRTOS. If he's into security, then starting with one of the SSL implementations might be good; if databases were more his thing, Postgres; etc, etc.
He should also become visible in the community he'd like to get work from. I'd suggest specific product forums (whether that's gitter, IRC, mailing list, or whatever) are much more likely to be productive in terms of establishing a profile and demonstrating expertise than more general things like Stack Overflow.
It's also probably worth looking at some of the freelancing sites (eg. freelancer.com): it's very hard to stand out there if you're a React dev, but it might be the case that C work is less competitive?
In my experience, developing deep and narrow expertise in a specific area helps land contracting jobs. If you're a generalist, it's much harder to stand out from everyone else. Perhaps that's a viable path here?
If you mean K&R C as a shorthand for “plain old C” then there’s a lot of it going on everywhere. Embedded and industry especially.