I feel as a chessman must feel when the opponent says of it: That piece cannot be moved. 
Debate with such an absurd position seems, to me, to be fruitless. Certainly the scientific community (by which I mean most geologists, astronomers, physicists, etc living today) supports a theory of a round earth (or globe); in fact I could find no credible scientists that holds an alternative position. In fact the Flat Earth Society (FES) rejects scientific evidence and scientists themselves as "the same old gang of witch doctors, sorcerers, tellers of tales, the 'Priest-Entertainers' for the common people. 'Science' consists of a weird, way-out occult concoction of jibberish theory-theology...unrelated to the real world of facts" . Truly I feel like Kierkegaard's chessman.
Instead of entering into a debate with the FES, I will focus on attempting to explain it. The FES has constructed a complex and convoluted rationalization to explain (1) how the world really is and (2) why everyone else is mistaken (see ). I think that this phenomenon may be understood in light of Weber's construct of "rationalization."
Weber's Process of Rationalization 
1. Rationalization comprises clarification, specification, and systemization of ideas
2. Rationalization comprises normative control or sanction
3. Rationalization comprises a conception of motivational commitment
Also, once a religion is sufficiently rationalized (systemized and unified), its core ideas come to have a logic of their own . The beliefs of the FES seem, in part at least, grounded in an extreme view of Creationism. In an interview with Charles K. Johnson - The President of the International Flat Earth Society - Robert Schadewald noted "Johnson's beliefs are firmly grounded in the Bible. Many verses of the Old Testament imply that the earth is flat, but there's more to it than that. According to the New Testament, Jesus ascended up into heaven" .
The concept of 'A Flat Earth' seems to come out of a tradition of Creationism and is 'rationalized' by its adherents in the face of overwhelming scientific evidence and consensus. This 'rationalization' creates its own sense of logic and solidifies (or riefies) a sense of reality through repetition and participation (in the Eliadean sense ) in which 'profane reality' is discarded for the construct of "mythic ontology.'
In short, good luck opening their eyes to reality.
I conclude with this thought from Weber:
Prophets and priests are the twin bearers of the systemitation and rationalization of religious ethics. But there is a third significant factor of importance in determining the evolution of religious ethics: the laity, whom prophets and priests seek to influence in an ethical direction. 
 Kierkegaard, S. (1987). Either/Or: Part I. Hong and Hong trans. Princeton, NJ: Princeton University Press, p. 22.
 Weber, M. (1993). The Sociology of Religion. Talcott Parsons trans. Boston: Beacon Press, pp. xlii - xliii.
 Ibid. p. xiii.
 Eliade, M. (1991). The Myth of the Eternal Return. Princeton, NJ: The princeton University Press, pp. 34 - 48.
 Weber, M. (1993). The Sociology of Religion. Talcott Parsons trans. Boston: Beacon Press, p. 45.