I don't really care about some rule of who has the burden of proof. For all I care, both sides have to provide proof. For the Round Earth, lots of evidence: The change of perspective as the viewer's altitude rises, the shadow of the earth in lunar eclipses, the timing and effect of tides, the angular effects of views of the stars as we travel north or south, measurements that work only on a sphere, views from space vehicles, etc. etc. On the side of the Flat Earth, not so much: Accusing all scientists of taking bribes, accusing all governments of being part of some vast ancient conspiracy, etc.
The Flat Earth side cannot even provide a reliable map on flat paper of what is supposedly an equally flat earth.
To me, the debate is decisively over.