I first heard about the Flat Earth Society in my 8th grade math class in 1961. The Society was first organized in 1904 in England, died out several times when its founders died, and is back in another iteration now
The origin of the Flat Earth Movement was an 1838 experiment to measure the curvature of the earth directly on a six mile straight stretch of canal known as he Bedford Level. A boat was rowed the 6 miles with a flag 3' above the water. The flag should have been 11' below the horizon at the end, but the entire boat was still visible, suggesting that the world is actually flat.
The result was due to refraction due to the observing telescope's having been placed only 8" above the water. No less than Alfred Russel Wallace accepted a challenge in 1870 to prove the earth was not flat. He had been trained as a surveyor, and knew about the refraction problem, so he placed poles 13' above the water at the 3 and 6 mile points, and set a theodolite at the same height to sight them. As predicted from a 25,000-mile earth, the middle pole appeared to be 3' higher than the end points.
It is indeed ironic that a YEC can see fallacies in flat earth arguments, but not in YEC ones.