None. Flat Earth is characterized by their denial of science. By performing empirical experiments then rejecting the results.
That is antithetical to the very core of science. So any scientist who is given experimental data that contradicts their theory is, should make new theories.
There's nothing fundamentally wrong with saying the Earth is flat, and then thinking about the implications, and then verifying the implications match reality, and then when you get bad data you modify your hypothesis. We need creative and curious minds to challenge the status quo with new measurements data and science. It's the rejection of empirical data that is the death of science