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You can get library books on your kindle, you just need to use a phone app

Why would you need a phone app? You can just email them to special Amazon email address and they'll be converted and uploaded to Kindle.

PS: Yeah that wouldn't work for books with DRM. So might be its the problem.

Library books also work on Kindle ereaders. I’ve borrowed a few that way.

That doesn't seem like a solution, but a work-around. I'm sure it works fine, but why should that extra step be necessary?