Most books downloaded by Kindle for Android these days are in the incompatible KFX format. Some books will still be delivered in MOBI or KF8 format, but these are stored by K4A with a .prc extension. I don't know how calibre deals with that. Also, DRM can be problematic.
Hopefully you still have your Kindle registered with Amazon. Even broken it is useful since it allows you to use the method Kovid described above to download books from Amazon.
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