To my mind, there are a few major problems with the "NASA conspiracy" idea.
1) It would have to involve every space agency - both public and private in every country that does this stuff. That's a lot of organizations. People like Elon Musk would somehow have to be muzzled when they first started to spend their own money to get into space and discovered the clear inconsistencies in their launch data.
2) It would have to go beyond just the space agencies themselves. Their contractors, the data analysis people, people like me who make software simulations of their systems.
3) TFES claims that NASA (and others) do this because of the money they get paid for doing space-related activities, and to keep earning it, they have to fake a round earth. But worldwide, the private space industry earns about $120 billion a year for their shareholders. So somehow these agencies have to produce more than they consume. Elon Musk would have had to be convinced to keep making fake launches and to make plans to go to Mars.
4) Why would governments allow people like Virgin Galactic and SpaceX to start offering to take people up into orbit (and later to the moon and Mars) when this would only widen the conspiracy to more and more members of the public?
5) It would have to involve a VERY large number of people. Not just employees - but people who supply equipment, people who analyse data,
6) Astronomers are acutely aware of the roundness of the Earth - they would be unable to operate space telescopes - or even accurately point their ground-based equipment to examine the universe without being a part of the conspiracy.
7) The conspiracy would have to go back in time too. People who navigated by the stars and travelled long distances in sailing ships would have been acutely aware of the vastly longer distances they had to travel in the southern hemisphere than in the north - and all of their books and instruments relating to navigation would have to have reflected that. Almost all sailors below the very lowest ranks would have had to learn this stuff - and then every single one of them would have had to know that there were two sets of books on navigation...two sets of charts...one faked, the other real. Every single one of them who wrote stories of their travels would have to have been lying about it. Even the rebels - pirates - people at war with each other - merchants - every single one of them would have had to be in on the conspiracy over at least 400 years...and not ONE of them spoke out!
Modern day international airlines and long distance shipping companies would have to be a part of it. Ships only travel just so fast...and to get from A to B in the expected times, so that freight would arrive in a timely manner...that would require them to understand the shape of the Earth. So everyone at WalMart who orders products from China, Indonesia and Korea would have to know that the Earth is flat and be bound to keep it a secret.
Basically, an insanely large percentage of the people of the world over the last 400 years managed to keep this secret from their families. Nobody blabbed in all that time.
It's not credible...it truly isn't.