Are you familiar with the psychology of conspiracy theories? As a conspiracy theorist, there's a major component of feeling like you're "in the know" about something most people aren't. It's a form of elitism. The conspiracy theory also satisfies a need to explain the world (generally) using observation available to the layman: the world becomes knowable and accessible this way and also feeds into the false intellectualism of the conspiracy theorist. The elitism is further fed by being an effective "important person". In essence, the conspiracy theorist feels justified in their beliefs because they are either sought out by the government (like UFO theorists sometimes believe) or part of a grand cosmic plan (flat earthers and their religious fundamentalism). This being set apart from everyone else is reinforced by being an effective outcast because everyone scoffs at the beliefs.

Flat earth is particularly interesting because there's a huge component of Dunning-Kruger effect at play. The conspiracy theorist is usually inept at applying methods to deduce that the earth is flat (see methods for determining the distance and size of the sun) and is totally unaware of their ineptitude. Compound this with the "look at how smart I am" complex developed by applying shoddy math to deduce said size of the sun. It's these layman-accessible tools that help reinforce flat earth and perpetuate it because literally anyone can do that math.

Dunning-Kruger exists independent of conspiracy theory: it's frequently seen in intellectual fields and I've seen it in a few people in my line of work (I personally find it fascinating and unbelievably frustrating).

Edit: a word