It depends on where you draw the line (heh) on "straightness" and "flatness". Some planes on gems or geodes are pretty flat, but probably not perfectly flat. Another example is a spider's web between two points. That's a pretty straight line if it's taut, but again, probably not exactly perfect.
Nothing is perfectly flat, neither in nature nor man made. It's purely a mathematical concept as every surface has some form of texture if you look close enough.