How do flat-earthers argue against these facts? [...]
The exact how doesn't matter, really, it's all about the that.
I've had the questionable privilege of growing up with a father who's never come across a conspiracy theory he doesn't like. Lizard royals, 9/11 was an inside Job, moon landing hoax, Bilderbergs, Rothschilds, JFK was shot by Ted Cruz' father, ... you name it, my dad buys into it!
He has 'evidence' for all of it and it's all rather easily debunked. I actually ended up being a reasonably good debater thanks to all the practice I got in my youth - but I never once dissuaded my father from a single one of his convictions, no matter how overwhelming the evidence to the contrary.
This is because, in essence, conspiracy theories are faith based beliefs. You're not going to find much proof of Jesus turning water into wine either. In fact, the entire discipline of chemistry stands in evidence against that claim - and yet millions believe it nonetheless.
Long story short, there's about as much point in questioning the rationality and intelligence of conspiracy theorists as there is in the case of people who insist that Mohammed flew to heaven on Al Buraq. People are not usually, in essence, religious because they find the empirical evidence compelling - they are convinced by the evidence any believer in another faith or none dismisses because it matches their preconceived ideas. I have a distinct feeling that this applies to conspiracy theories as much as it does to religion.