Audible is not a streaming service. You can register 4 devices with your Audible/Amazon account (Audible is owned by Amazon).
You can access your library from any or all of your registered devices and download the books. If you delete a book from your device, it remains in your Audible library online, and you can re-download it as often as you want.
If you buy a new device (I use may Android phone as my primary device), just install the Audible software, register it to you account, and start using it.
If you dispose of a device, just un-register it from Audible, so that you can register another.