It has nothing to do with the FE theory, as flat used in the context of the geometry of the universe sort of means something different. For the universe to be described as flat, triangles must, even when extended out for millions of light years, only have internal angles that add up to 180 degrees. If the universe is negatively curved then it is hyperbolic, meaning that straight lines end up diverging and getting farther apart (but on scales nowhere near small enough to have relevance at the earth's scale). If the universe has positive curvature then straight parallel lines will eventually curve in on each other and intersect. This kind of curvature is more general though than the shapes we associate with the earth and makes claims on longer scales than earth's. The current theory is that curvature is determined by the average density of the universe (more massive universes of the same size ought to have more curvature).