Can you connect a Kindle audio book to the auxillary port to get the sound thru the car speakers?

Yes, you can, but, please keep in mind the following important caveats. It would be better to use a newer Kindle that has LTE or you'll have to download the book before you start and it would sound better with a newer Android version. Better yet, go the Google Play store and install Kindle on your newer Android phone. Then plug the phone into the car's auxiliary jack just as you would to listen to music or Sirius radio. You'll have to turn the volume up on both the phone and the car's audio system, but, you should be able to hear something. My Kindle is the first edition, a pathetic Android version of Gingerbread, 2.36. My Android phone is much newer and while I didn't try it, I listen to Google Play Music with no problem. If you can listen to music, you should be able to listen to voice on your audio book as well. Oh, in case you don't have "Audible" which by the way is the best audio book application to have, get it, you'll be glad you did, it's the best in terms of control and selection. Once final thing, you can be a "lite" member of Audible. They have different levels, and pricing ,so you don't have to spend a fortune on that if you only listen to books once in a while.

More, the quality of your audio system will have a major impact on your listening pleasure. If you think it's going to be the same as plugging in your Bose noise cancelling head phones at home, think again. You have to adjust your expectations when you're in the car with noise from the road, engine and other distractions caused by drivers and emergency vehicles.