A story about people in a flat world would be very boring. People would only be able to see a single line, since they would be compressed into a 2D form. To better explain this:
As 3D beings, we can see all of a 2D shape. So we can see every single side of a flat square, circle, triangle, etc. However, we cannot see all sides of a 3D shape: we cannot see every part of our phones or computers at once, for example. If we were in a 2D world, we would only be able to see part of any other 2D shape, or a 1D view. This means that we would only see lines of varying lengths and colors, but everything would be infinitely thin and it would be very hard to see much at all.
It would also be incredibly different to expel waste but I won't even try to get into that.