This has been answered already but, You have to consider, that egg has to squeeze out the females hindend, so they are not all that fragile.
From what you discribed, it sounds like a poor nesting, so if the egg fails, it may not have a thing to do with you flipping the egg or not.
With most eggs, they can be flipped or moved, but there are certain times when they cannot be. With kings, there is normally a good degree of embryo growth before the egg is deposited, So they are less prone of injury then some other types of reptile eggs. Also its more about speed of movement, then actual movement. They can be moved or rotated slowly.
You will see here that folks mark the top of eggs, thinking thats a good thing. If you think about it, the embryo normally migrates to the top, so that would be about the worse place to mark, the sides are much safer.
But then even writing on the top does not often cause a problem. hahahahahahahaha good luck