I want to make a simple, interactive gallery app that I can install on my Kindle.
Is that a thing?
If you're referring to an eink Kindle, to my knowledge you are out of luck since the device does not support interactive content like that in an EPUB.
The Android-based Kindle Fires do support EPUBs and interactive content. Typically you would export a Hype document and include it in you epub's XHTML via an <iframe> element (since Hype documents are HTML5 and cannot be used strictly within an XHTML context). If you search for epub or epub3 on the forums you'll find a lot of topics and information on this.