For the record, and for those it might help, this is what I do... (but of course I know all do not have iPhones!)
I open the browser on my phone, go to Librivox.org, select a book, click the RSS button. This opens the Apple Podcasts App and I click subscribe. Then, If I need to download I can, or just let it stream without downloading. The advantage of this over the Librivox App is I can listen to multiple books at the same time, and it saves my spot in every one of them.
You know, listen to one with the kids, one with the husband, one with just the girls, one while driving, one at dinner, one while sweeping, cooking, vacuuming, while taking a bath... OK, TMI

But doesn't anyone else multi-task books this way or is it just me?