Prince Prospero is a flat character because he is not well developed in the story. He is also a static because his viewpoints do not change in the story.
The uninvited guest(the antagonist) is a flat character because we only see one side of him which is him as a villain, and he is static because we don't get to see his views and they don't change.
Point of veiw
This was an extensive and magnificent structure, the creation of the prince's own eccentric yet august taste. A strong and lofty wall girdled it in. This wall had gates of iron. The courtiers, having entered, brought furnaces and massy hammers and welded the bolts."(78)
"the Prince Prospero, maddened with rage and the shame of his own momentary cowardice, rushed hurriedly through the six chambers, while none followed him on account of a deadly terror that had seized upon all."(83)
This story is in 3rd person limited, we can only see the feeling of the prince and no one else throughout the story.
This story has a very creepy and strange mood. This unknown masked man is very creepy and no one knows how he got there, creating this mood for the story.