Do flat-earthers think that men have gone to the moon and that we have rovers on Mars? Or do they think it is all a hoax?
.Good question! Flat-earthers generally apply their de facto skepticism toward everything they can find to which it might seem to "stick." They don't think that mathematics is credible unless it can be used to argue in favor of their pet hypothesis (even if it is used incompletely or incorrectly). They usually deny the existence of satellites or space flight of any kind such as the International Space Station (ISS - which can be seen in orbit using simple land based portable telescopes when you know how to read the updated Ephemeris of the Station, or almanac, which is available for free online). 
It's therefore not too hard to understand that they would likewise doubt the various missions to the moon, or to Mars, or probes sent beyond Mars like Pioneer or Galileo, etc. This is largely due to their mule-like dogmatism for the existence of their so-called solid firmament (which is not called by any such name in Scripture nor is it measurable, testable, verifiable or found by anyone, ever). Notice, they cannot prove their "firmament" exists as they think it does (solid, not a metaphor used to describe the atmosphere and region beyond it all the way to the nearest stars as the Bible footnotes describe it), nonetheless, they accuse anyone who disagrees with their flat-earthism of lying when they use information or data obtained by satellite or sophisticated equipment like radio telescopes or cameras on the ISS.
.
Since so much questionable material has been identified regarding the lunar missions (such as some faked studio shots of the lunar landings) some who have no vested interest in flat-earthism (such as Matthew, the owner of this forum) have decided that perhaps the moon landings are not ALL of which we're being lied to about, and therefore hold open the possibility that perhaps the shape of the earth is up for grabs or whatever.
.
I find it odd that my many descriptions of the very simple steps anyone can take to personally verify the layout of the sun and moon relative to the earth which can be directly observed with our own eyes without fancy equipment is for whatever reason insufficient for these armchair doubting Thomases.
.