The idea that the Earth is flat emerged primarily as a counter-movement in the 19th Century. Still don't quite understand why, exactly. Reaction against the way Society was moving, most likely. Prior to that, there was never a point in recorded history where the accepted view was for a flat Earth. So actually the progression is:
- Earth is round
- Actually it's slightly bulging one way or another, we don't know which way (poles or equator)
- It was the middle, in fact.
And since then the measurements have got more accurate, but nothing's changed or is going to. The corrections to a round earth due to the equatorial bulge is of order 0.3%, so can be neglected in both cases anyway.
/off-topic.