The standard flat earth answer is that all of the continents we know about are on the same side (and therefore the map of the world is like the UN map, with what is commonly known as the north pole at the center and the south pole spread around the edge).
No-one knows what's on the other side, according to the standard flat-earth model which I have observed here.
You would not, therefore, come out in China if you were digging down from America; since China is, of course, on the same 'side' of the Earth as America, this would be impossible. You could probably dig your way there, alright, but it wouldn't be straight down.
Since no-one has managed to dig to the other side, what's down there is unknown. And don't bother citing photographs taken from space: they're all part of a conspiracy that the Earth is round, remember? :wink: