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Libby is able to sync with your kindle, and then you just choose “send to Kindle” on your phone when checking a book out and the book will appear in your Kindle library.
https://help.libbyapp.com/en-us/6017.htm
If you have a Kindle, this is 100% the best way to read books.
After pouring the detergent into the appropriate receptacle, toss the cap in with your laundry to be washed like everything else. No mess.