Audible app compatible with iPod Nano

There are no third-party apps for iPod nano. iPod nano has built-in features that are like "apps," but it does not run iOS. You cannot add new features by installing additional apps, like on iPod touch and iPhone.

You can play audiobooks on iPod nano, by syncing them from your iTunes library. If there's a way to add audiobooks from Audible into your iTunes audiobooks library (without restrictions), you may be able to sync them to the iPod using iTunes, and play them on the iPod. Other sources for audiobooks include iTunes Store, audiobooks imported from physical CDs, and audiobook audio files downloaded from other sources (and added to iTunes library).