For the “I want to have a proof that would not require travelling more than a couple of kilometers” part, I would look at seismology, in particular seismic tomography (<a href="https://en.m.wikipedia.org/wiki/Seismic_tomography" rel="nofollow">https://en.m.wikipedia.org/wiki/Seismic_tomography</a>)<p>It allows us to ‘see’ the other side of the earth.<p>Given enough locally made samples, I doubt there is a model of flat earth that explains them.<p>But of course, as others have said, it’s not possible to reason with somebody who doesn’t accept logic as a requirement for ‘reasoning’. A flat-earthed might, or example, accept the tomography proves the existence of a spherical object, but claim the earth is just a small (almost) flat part of the surface of that object.