How would I go about approaching the Dean in this situation?

Before you approach the Dean (or anyone else in a position of authority over your professor, like her department chair), you need to try and work this out with your professor. Tell her that you understand if the Kindle's not up for discussion, but you're deeply hurt by what she's said, and you'd like to know not only what's given her that impression but what she'd like to see you do to improve. If she continues to respond with disparaging comments instead of offering constructive suggestions, then you can complain.