That creates a large population of people primed to expect scientists to be lying to them. Flat eartherism is harmless in itself, but I suspect that the OP's father also believes several other conspiracy theories -- and votes according to them.
That doesn't change the OP's problem, or your observation that you can't fix it. But if you can't even solve the readily-demonstrable fact that the earth is round (just phone a trustworthy friend a few timezones away and ask where the sun is), how are you going to get people to agree about things that actually cause harm?
The problem starts when some ideas are not harmless. For example idea that covid is dangerous. Some people don't see evidence of this around them (myself included, I don't personally know anyone who had covid), so they don't believe experts, so they don't protect themselves and others. Some people even have idea that they are in the right, experts are lying and they need to actively prove that experts are lying in any way they can, even misrepresenting facts.
What changed your mind? :)
“Figured out” was a poor choice of words because I didn’t have an epiphany, “learned”would be more accurate.
It is very important for some people to convince others that their ideas are correct (which they very well might be).
Let go of this "I need to convince people to agree with my view." Instead, love your father for his other qualities and allow him to have his harmless ideas.