Geocentrism is a perspective placing the earth in a preferred location in the universe. There is substantial observational evidence that the earth is in a preferred location in the universe, and The Principle is a documentary that discusses this observational evidence in the context of the Copernican Principle. Many people are attacking The Principle, and some of that attack is being waged by confounding geocentrism and The Principle with flat earth ideas.  Please see this article:

Flat Earth is a PsyOp to Attack Documentary “The Principle”

I wanted to discuss the differences between geocentrism and flat earth ideas. First let’s discuss the types of geocentrism that exist:

1. Scriptural geocentrism originates from Scriptural references indicating that the earth is stationary and that the stars/planets move around the stationary earth; Non Christian ad non Hebrew sources also supported geocentrism (as well as heliocentrism) in ancient times just based on reason.

2. What I will term scientific geocentrism is just the idea that the earth (or by a stretch the Milky Way) is at or near the middle of the universe. These ideas are supported in some modern cosmological studies.

3. Observational geocentrism is the interpretation of observational evidence of alignements between the earth and the universe at large, and other observational data supporting a special position of the earth in the universe. It can be used as a means to falsify the Copernican Principle. This can be stretched to galactocentrism.

The Principle largely deals with observational geocentrism; though Scriptural geocentrists weigh in on the discussion, and scientific geocentrism is considered. The purpose of this article is not to expound on geocentrism, but I wanted to lay out the scope of the topic.

Flat earth similarly derives from Scriptural passages and has been supported in ancient times by non Christian or Hebrew sources. It is my opinion that flat earth fails the observational category, so I will not talk about observational flat earth. It would be difficult to imagine a scientific flat earth also; though some claim to propose such theories.

So basically any relevant ties beteeen geocentrism and flat earth are strictly at the Scriptural level.

Basically, the relationship is in the beginning chapters of Genesis (I am ignoring passages that discuss the four corners of the earth and other obvious analogies). Flat earth advocates interpret some of the descriptions as the earth being a flat surface covered by a hard dome. Using the same passages religious geocentrists interpret these passages as a description of a plenum that describes the earth and the universe. These plenum interpretations are consistent with some aether type descritpions of the universe, and are consistent with the Scriptural passages. From a Catholic perspective, the Church has never given any official credence to flat earth theories, but certainly has to geocentrism. For more information about the Scriptural interpretations related to Genesis and the plenum, I suggest stopping by Robert Sungenis FB Page and drop him a question. He is probably the best Scriptural scholar on this question.

Ask Robert Sungenis About Geocentrism

The conclusion is there is only a Scriptural debate within Genesis between geocentrism and flat earth, and I will add that physical evidence proves that the plenum interpretation is the only viable one. From any other perspective (scientific or observational) there is no connection whatsoever.