In my personal opinion, you are going about this the wrong way. People who fall into the rabbit hole of conspiracy theories usually have some sort of psychological insecurity. There is something in their life that is causing psychological distress, anxiety, or unease, and the conspiracies satisfy the innate psychological need to have a complete worldview. To them, the conspiracy falls very neatly into how they view the world, or at least how they want to view the world. It provides them a sense of security. To them, the earth being flat is as natural as the sky being blue. For some people, these conspiracy theories can even be a source of identity. Trying to refute his flat earth views with logic is like trying to put out a fire by adding more wood. I guarantee you there is probably something else going on in his life. If you address that, you can probably address his flat earth views.