Flat is flat.
The shape of the earth has nothing to do with the flatness of an object.
The only change in flatness of a flat object in space brought to earth would be from resisting the gravitational field of the earth, and even that depends on how it's supported. If the support is at each end, it will become concave on the side away from the center of the earth. If supported in the middle, it will become concave on the side toward the earth.
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