Thanks for posting in the Community!
Currently, it's not possible to share an audiobook with Family Plan members. The purchase is bound to a specific account and can be used only with the account used for the purchase. With that being said, your kids needs to purchase the audiobooks they'd like to read through their own accounts.
More info about Audiobooks you can find in this support article.
Hope this clears things up. If you have any questions or need anything else, the Community is here for you.
Spotify needs to channge this it looks like this is possible with the competition. I also cant share a book with my wife, it will be my last purchase from them.
My husband and i agree. We will only be downloading on audible now. We assumed this feature was already available when he bought 4 books for our business, but they are not. But he has no problem with my audible library.
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