I've explored this path before and you'll find you have 2 options. You can run the Audible software under Wine, or you can run it natively inside a VM (VirtualBox) using Windows.
If you're interested in the Wine route take a look at the WineHQ page. Specifically this page, titled: Category: Main > Multimedia > Audio > AudibleManager.
Using this method you'll be extracting the `.aa` files out to CDs, from which you can extract `.mp3` files. Your path is basically `.wav` to `.mp3`.
You can try saving an actual CD by buring them to a `.iso` file which you can then mount and rip down to `.mp3`'s from there.
Because of the DRM the path is intentionally painful, making you perform various steps in a manual manner.
### References
* How to listen to Audible files?
* Audible Linux – How to Install in Ubuntu?