The characters in "the lady, or the tiger? are flat characters, who are more "types" than real people. why did stockton use this type of character in his story?

He didn't create realistic, detailed characters because his short story is an allegory. In an allegory, deep characterization is often not needed. It may even be redundant, as the story isn't about characters themselves and their personal dramas, but about the plot which is supposed to represent a general problem. In this case, the point of the story is human condition and impossibility to make the (right) choice.

The correct answer is a