Anything downloaded directly from Amazon that has DRM (most stuff from big publishers has DRM) will be keyed to your individual device and you'll have to redownload each book again to the new device. You used to have to do one book at a time, but they've added a select all to the website so you can do an entire page of the My Content & Devices book list at a time (IIRC it's 200 books at a time). Just go to
https://www.amazon.com/mycd and take it from there.
I should note that using Calibre doesn't automatically mean your books are DRM free, you have to set things up with 3rd party plugins if you want to remove DRM.