I'd like to have users input a single prompt, like "read me a poem," and have QnA give a different response every time. Ideally, QnA would rotate through a list of responses I've created. Is there any way to do this?
That's not really the best use case for QnA maker. QnA Maker enables you to power a question-and-answer service from your semi-structured content like FAQ documents, URLs, and product manuals. The QnA Maker service answers your users' natural language questions by matching it with the best possible answer from the QnAs in your Knowledge base.
What you are looking for can be done with a Chat Bot where you write the logic for rotating responses. Visual Studio has a echoBot sample pre-loaded that can help you get started and we have a good deal of documentation here: