Is there any way I can listen to my Audible books on my squeezebox?
There isn't currently any Squeezecenter plugin for Audible books as far as I can tell.
All there is are various workarounds to convert Audible's proprietary .aa format into something playable through Squeezecenter, such as MP3.
The least technically challenging is to use Audible's own feature to burn the books to CD, you can then use any of the many pieces of software with CD ripping functions (eg Windows Media Player) to rip this to MP3. This has downside that a CD can only hold 70-80 minutes of audio, and a book can be hours long.
Alternatively there are Squeezecenter plugins that can capture the output from your PCs sound card and redirect that to a Squeezebox, but that would mean that you'd still be controlling playback through Audible's software and wouldn't be able to use your Squeezebox's remote, or the Squeezecenter web interface to do anything more useful than control the volume.
Some of the options are listed here with instructions: Remove DRM from Audible's audio books (Removing copy-protection from .AA files).
Obviously you should be aware that deliberately circumventing DRM copy protection is illegal in some countries, and that you should definitely only do it for personal use on personally owned incompatible playback devices.