There is no such thing as "scientific method". Only school boy conception of science espouses such a view that there is a scientific method. What we have are a set of heuristics learned from the history of natural sciences. These heuristics function as guard rails: for instance, a theory that is postulated to explain already-collected facts is ad hoc; a theory should solve new problems; a theory should solve predict novel 'facts'; do not increase theoretical entities unnecessarily; do not try to explain away by postulating various sub-entities; do not confuse a description with a phenomenon; save the phenomena; etc.
When you or I drive/walk, what do we experience: flat earth, of course. In other words, both flat-earthers and spherical-earthers experience the same. Further, flat-earthers reason that if the earth were to be round, one would fall off of the surface of the earth on a sea/land travel. Since such an incident never occured, flat-earthers reason that the earth can't be spherical. Flat-earthers reasoning is not spurious, they are entirely reasonable.
How to help them, you have to make them pilots and fly at 50000 feet, and they can experience the sphericalness of the earth directly. In other words, you can't transfer knowledge via authority. That's why there are disputes about what sciences are? Are sciences reduced to a set of theories, or just experiments, both theories and experiments? What happens when one theory gets supplanted by another, better theory? These are deeper questions about knowledge.
When I am sick, I trust some or doctor about his knowledge to diagnose. In some cases, even patients start doing research on their own (you can find many stories on this forum) to figure out when the doctors are not helpful. No one creates chaos, if one is genuinely seek knowledge. Instead of seeking knowledge, one seeks fame, followers, etc. Or as the other commenter said 'when so much energy is spent trying to undermine one's opponent'. That's a different story.
We have to be careful about psuedo-winning against those who create chaos. Here is an interesting piece by Late Prof. Larry Laudan: "Science at the Bar--Causes for Concern" [1], originally appeared in Science, Technology, and Human Values 7 (41):16-19 (1982)
[1] https://faculty.washington.edu/lynnhank/Laudan.pdf