Academically the experience of a House of Mirrors effect is not a Kaleidoscope effect (which creates symmetrical patterns). A House of Mirrors is designed to trick someone within from finding the true path by the use of multiple mirrors and transparent and opaque walls to obscure the location of the correct path out of the maze (Often they are not even mazes... but labyrinths. The difference is that in Labyrinths there is a single unbroken path to the center, such that as long as you move forward, you will reach the center. A maze is a series of broken paths that may never lead to the center and your initial path may terminate in a dead end).
However, in this situation, it's purely being academic and this is perfectly fine if the speaker would not know this.
It would be correct to use the phrase "A kaleidoscope of me" as the word "Me" is the first person singular predicate pronoun. The First Person plural predicate pronoun is "us". By definition, there can never be more than one first person singular (even in a situation where you and your clone are interacting, your clone is their own unique person and thus would not be covered by your use of "me".... but would be covered under a use of "us").