For the sake of argument, let's all agree that the Earth is, indeed, flat. Now, let's also agree that the Sun and the Moon are flat. There's an assumption that every other body in the Universe, whether they be planets/stars/et cetera, are also flat. When we see these other forms that are also flat, we obviously see them at an angle where the flat surface is facing us all the time. Never do we see a planet's "side," we only see a circular form.
If it isn't clear what I mean, think of it like this - The flat Earth would probably resemble a cylinder, with the surface being circular, but not a sphere, and the underside probably also being a circle. On the "sides," there would be a few hundred mile wide boundary between the surface and the underside. This would be where the crust extends to the mantle, extending to the core, and opposite out towards the underside. If you saw this from the depths of space, it would look like a line. For example, look at a plate from the side. You can't see the surface of the plate or the bottom, so you have no way to know that these are round.
Now, if all other bodies in space are actually flat, this means they all face us all the time. We never see their "sides." How does every planet/star/et cetera in the entire known universe face us? Are we indeed the center of the Universe? Does the Earth emit some force which makes every mass in space face us in that fashion?
I know someone is going to bring up how galaxies are "flat" and we see that all the time. Well, a galaxy isn't a single mass. It's a collection of bodies in space. Saying that a galaxy is one hunk of mass, amounts out to saying that traffic is a single object, and it's not made up of however many vehicles are on the road, but instead stands by itself.