These claims have been thoroughly debunked by experts in the field of geodesy and astronomy. The main flaws in the flat earthers' argument are:

Misinterpretation of the data: failing to account for factors such as atmospheric refraction and the limitations of the instrument.

Lack of understanding of the Earth's shape: assuming that the Earth is a perfect sphere, when in fact it is an oblate spheroid, meaning that it is slightly flattened at the poles and bulging at the equator.

Failure to consider the scale of the Earth: the enormous scale of the Earth means that the curvature is very subtle and only becomes apparent over very long distances.

Ignoring the overwhelming evidence from other fields such as satellite imagery, GPS, and the behavior of ships at sea, which all confirm that the Earth is an oblate spheroid.