@FieryJack, thanks, but it appears you didn't read the question and the dozens of "me too!" The page you linked to is only the instructions for what to do. We're all saying "Yeah but it's not working." We need troubleshooting.
I'll add that I can get the book to play using Now Playing, but it won't play on my Bluetooth headset. Having done that, it will now play in the Audible app to my headset, but the controls don't work.
Later I'll see if I can get help from Audible. I know Apple isn't responsible for the functionality of apps developed by other people, though I do think there ought to be some obligation to make the stuff work if it's going to be approved in the App Store ... not your fault! :-/ Again, thanks.