If Aeroplane Mode is On, tap to turn Off. To do this: Tap near the top of the screen to open the Navigation Menu. On the left side of the screen, select Sync. To re-download a book, click the tick-box next to it to open a drop-down menu. To sync your Kindle app with your Kindle, open the Kindle app and sign in. Scroll down the page to see a list of all the books you've ever bought and downloaded for your Kindle.
I believe there is at least one wireless solution for connecting your Kindle to your Calibre, but in the end I stuck with using the USB connection, as by the time I need to move some books around, I need a recharge, so i get a two for one deal (load and charge). To update your Kindle to the latest software, you need to have WIFI enabled and connected to a local network. Once you're on the Amazon website, click 'Kindle' then 'Manage my Kindle' in the top navigation bar of the Kindle section. Once a week or so, I sit down at the PC, remove some books from my Kindles, mark them as read on Calibre (tag 'read'), add some new books to the appropriate kindle ('paperwhite' for reading in bed, 'keyboard' for text to speech while commuting) and tag the books I am currently reading in Calibre by the device they are on.
My 1263 (current count) works are stored on Calibre, I download from Amazon, Smashword, Baen, Project Gutenberg, etc. I won't go into all it's advantages but, essentially it is your own personal library, that you can organize and store you books on, regardless of where it comes from. The only disadvantage the Calibre has it is a bit more difficult to connect wirelessly to your collection. I searched for solutions and read many articles & blogs, I strongly desired an Amazon/Kindle solution, the majority pointed to a single solution which I eventually adopted. I was trying to keep track organized with an Excel book.
I personally have some OCD issues that require my books be in some kind of order that is not primary based on who I bought it from and when. If you have works from anyplace else, then the prospects get worse. If every book on your devices is from Amazon, then you can do some organizing at 'Your Account' > 'Manage Your Device' > 'Your Kindle Library' or by using the cloud. I am guessing you have already found Amazon's Organizing Your Kindle Content.