Why couldn't gravity work on a flat earth?
First problem, if gravity existed on a flat earth, then gravity would cause the earth to be pulled into a sphere.
Second problem, gravity pull is greatest in the direction of the center of mass. This is fine on a round earth since we are being pulled toward the center. But, on a flat earth, the farther you get from the north pole, the more you will be pulled at an angle. Things would not fall straight down, but at a slight angle that would increase as you move towards the rim.