I know that you've switched from talking about Dropbox to a focus on calibre, but I wanted to answer the original question fully just in case anyone else asks.
When it comes to connecting Dropbox to your Kindle account ...
There's IFTTT:
http://the-digital-reader.com/2015/0...o-your-kindle/
And Wappwolf might also work:
http://the-digital-reader.com/2015/0...drive-dropbox/