I never heard of Plato's cave before reading this thread, so I probably don't understand it as well as you do, but I still clearly see that you mention the idea of knowing the earth is flat based on what you see from the surface. Given the size of the earth, we know that a round earth is possible, and doesn't contradict our senses. If you mean that someone who has not traveled the earth, and has no idea how large earth actually is, they probably couldn't imagine the actual size of it, or the subtle curvature which could eventually form a sphere. If you limit the size of the earth to what you have seen, then I guess you might think the earth is flat like the people in the cave think shadows are real. Was that your point?
That's half of it. The other half of my point was that as long as we are confined in our local frame of reference on Earth, we can never know the Earth?s true shape, be it flat or round. Maybe the truth is that it is indeed flat, that NASA is feeding us with nothing but shadows and illusions. Or maybe not. Its size is irrelevant, because it can be a very big cylinder or sphere. It doesn't matter if the person has traveled around the Earth or not; no matter how far he travels, he still sees the ground being flat, mainly because he is still confined in a local reference frame on Earth. On the one hand, he perceives and interprets the Earth being flat due to the flatness of the ground wherever he goes. On the other hand, he perceives and interprets the Earth being round due to the sinking ship effect.
Thus, since we can never fully determine the shape of the Earth in our reference frame, I argue that its shape is meaningless.
Now, if you want to enlighten these Flat Earth believers, raise some money and send one of them into space, just like how one of the prisoners in the allegory reaches the ultimate reality and sees the light. Otherwise, they will have to believe that the Earth is flat due to their sensory experiences, since it is considered insane to lose faith in our own senses. That's part of the main thesis of Zeteticism: never accept what you're told by anyone until you see it for yourself.
As I've stated before, the allegory of the cave can be both a critique and tool of FET: the shadows can be those we see outside our window or those distributed by NASA, respectively. The truth is out there.