I specialize in the history of food (and environments, culture, medicine, and the body) in modern Britain. I teach at three different institutions, I write and research as much as I can. So, basically, we make a living like most other historians, either in thr academy like me, or in related industries like museums and archives.

are there really food historians?

Mark Kurlansky has written a number of food histories on a variety of subjects (Cod, Salt, Oysters, a biography on Birdseye the frozen food magnate, a history of the WPA project on American eating habits in the 1930's, a history of the fishing town of Gloucester, and various food passages in his other books). There's also Empires of Food by Andrew Rimas and Evan Fraser, which is a bit preachy when it comes to politics but pretty well written. So there are definitely food historians, of which the above are merely a selection of books that I have liked.

what do they do? And how do you make a living as one?

You can write books (which generally doesn't leave you rich). As with most "popular" histories they generally are lighter on the footnotes and original research and heavier on narrative, but that's not necessarily a terrible thing. You can also be employed by a company to research, archive, and write about its history with food. You can also teach and do research as well.