Stream Audible audio to DLNA/UPNP speakers
So I got official response from Audible team: 

It's Bluetooth, Auxiliary Input (audio jack, ie wired speakers) or ..burn a CD! 

UPnP/DLNA - not mentioned.

So it's Bluetooth I guess for me. Not the preferred option :(

For for completeness' sake, here is precise citation from Audible Customer Service team email:


  Bluetooth
  If your mobile device and speaker support Bluetooth, your audiobook's will play through your speakers similar to how a phone call comes through via Bluetooth. The Audible app must be open and all functionality for the audiobook (changing chapters, narration speed, playing, pausing, etc.) can only be changed through the Audible app on your device.