I've gone ahead and drawn 3 pictures (not accurate at all) of what some maps I've seen look like, and how they depict the Earth being flat.

The first image is just the badly drawn depiction.

The second image is plotting 2 points in a straight line, as if someone were flying from Point A (in the Americas) to Point B (In Europe).

The third image is where the question comes in.

What would happen if someone were to fly from Point A to point B in a straight line (flying East in a straight line), and always flying in the same direction, flying to Point A again. Assuming that there is an edge to flat Earth, would a plane flying East across the Earth hit an edge or would it reach the Western side of the Americas?

Another question: If we were to draw a diameter line on a flat map of Earth and fly on it, would we reach an edge/border?