Amazon has a beta plugin for Adobe InDesign versions CS4 and above that make it easier to export InDesign books to the Kindle mobi format. The plugin is available from the Kindle Direct Publishing Help page here:
Download the plugin. Make sure InDesign is not open, and run the .exe file to install. There is a Mac version, too. While you are at the KDP page, download the Previewer to permit easy viewing of mobi files as they will appear on various Kindle devices.
InDesign has a plugin for Adobe Digital Editions export to ePub format. Though you can convert ePub to mobi uisng Calibre, the results require a lot of editing to fix formatting issues. The new Kindle plugin reduces, but does not eliminate the editing required to produce a Kindle-friendly mobi file.