Flat Earth: The History of an Infamous Idea by Christine Garwood is a good read, although getting a bit dated by now. It's written with a considerable Round Earth bias, but then again, what isn't?
Kelly Weill, a reporter for the Daily Beast, is currently working on a book of her own. I obviously can't comment on the content, but she seems quite active and thorough in her research, so I'm cautiously optimistic. let's see if I get to eat these words once it comes out