Flat earth is a model that I believe to be derived from the Christian cosmology. I don't concern myself much with the materialist worldview that is without a centre to orient but in phenomenology, meaning as the human experiences the universe, the world is experienced much as s dome around his consciousness. That results in something below, the earth which is experienced as a flat plane and the dome of the sky. In Christian language "earth" means all physical things including flesh and stars, while "heaven" includes concepts, ideals and principles etc.

So once one discerns the two worldviews, the "round earth" of modern day science and the "flat earth" of ancient cosmology do not contradict but instead work from different anchor points and explain different aspects of being.