I have no knowledge about this from before, but I was curious and started reading the wiki article (so take that as what you will).
If we're talking about the origin of theories of the Earth being flat, there are multiple, over various time periods. Focusing on the Modern Flat Earthers it seems to originate from Samuel Shenton in 1956, London. In 1972 it reached the US.
However, there is also a section about the "Internet-era resurgence" which mentions how the flat earth craziness spread via social media. Which is international.
Basically, however one would put it, I'm fairly certain we can say it didn't originate in the US. But again, this is all from the wiki page, and I'm not that interested that I'd bother to actually research the topic, so please do correct me if I'm wrong.