Is a smoothly paved sidewalk straight up a hill flat? Can the side of a hill be flat? Are all sides of all hills flat? Flat and level are not identical concepts. (My big dictionary has 101 definitions of flat; and, 60 definitions of level). One example of what is flat is a 2-D surface in a 3-D space. One definition of level, using a bubble leveler, is perpendicular to a point vector of gravity. Using a bubble leveler every 20 ft. or 6 meters, you could build a ‘leveled house’ completely around a planet. Light from a laser leveler follows the curvature of space caused by mass; and, like a bubble leveler, can be accurate enough over short enough distance.
Mathematically, what is flat is a geometric in all dimensions that are lower than, and when present in, an n-dimension. In the first (1-D) dimension, zero dimensional points are flat. In the second (2-D) dimension, zero dimensional points and one dimensional lines are flat. In the third (3-D) dimension, zero dimensional points, one dimensional lines and two dimensional surfaces, which is a common understanding of flat, are flat. In the fourth (4-D) dimension, a 3-D sphere is flat. For example, in an n-dimensional space, an object of less than n-dimensions has been flattened in one or more physical dimensions. In dimensions that are more than 3-D, we are all flats, perhaps being either flat wrong or flat right about the existence of dimensions that are more that 3-D.
Whoever originated the words, flat Earth, should define flat Earth. From what I read, flat Earth sometimes seems to be a denial, a refusal or a rejection, as in, “I reject that authority on me”, or, “I refuse the authority of science”, for some reason.