Load books collection from Kindle Android App

[paroariax]

Apologies for a newbie question but I'm trying to figure out if Calibre is for me or not.

I want to better organise my Kindle collection. I don't have a real Kindle device, just a rooted Nook running Kindle For Android. When I connect via USB it tells me there's no e-books on the device, which is of course true if it's looking for files on the SD card. I was under the impression that Calibre could read the titles of the books in the Kindle app. Why else did it get me to select that I have an Android tablet with Kindle app when I first ran Calibre?

The FAQ talks about sending e-books to the device by copying them to the SD card, it mentions nothing about reading the Kindle books already in the app.

I tried downloading the Kindle books from "Manage Your Content and Devices" on the Amazon website, but that tells me "No device is eligible for downloading the selected content". Does downloading only work if a have an actual Kindle plugged in?

Thanks guys, can anyone suggest something I can try?