NASA has been the 'fall guy' for a conspiracy theory that is too big to be successful. The rate at which current science is expanding, to the point where the common Joe can launch go-pros in high altitude balloons and dozens of companies across the world are planning and getting ready to launch privatized space flights for fun and profit, there would simply be too many people on the 'inner circle' of such a secret.
The idea that there is an alternate reality is attractive, very much so- but this particular theory is only sustainable if you willingly suspend disbelief and ignore certain evidence while cherry-picking at some others.
Look- the fact of the matter is that if you spend any time here, you'll get some excellent (albeit long-winded) evidence that supports a flat-earth theory. If you dig though, you'll see that there's a lot of scientific data that is relied upon to prove the flat earth that is little more than proof of concept in a lab, but without any legitimate citation of real-world application.
Cosmic Ray devices and the Biefeld-Brown effect are magnificent examples. Proven in a lab, but nobody can point to it being used outside of a controlled experimental setting.
Poisson's Spot is another one- this one states that light from the sun would curve around a round earth and make it daylight all the time, even on the back side of a globe. Dig for five minutes though, and you'll see that this experiment relies on a very specific set of circumstances to work- circumstances which need to be ignored completely in order to apply it to a flat-earth theory.
Theoretical science is given a lot of credibility by the flat earth community. Couple that with the fundamentals of the Zetetic method which draws scientific conclusion from observation (It looks flat so it is flat) which can be easily misinterpreted or manipulated, - and you've got a lot of ammunition for an alternate reality.
Good luck drawing your own conclusions, but I highly encourage you to dig deeply, VERY deeply into any evidence you're given...from either side. Questioning is learning, and even if you learn that the earth is not flat, you'll pick up a lot of other stuff along the way.
Cheers.