To come back to the topic there are nice ways to get the content of your dropbox library to your kindle.
If you use calibre to organize your library you can use
calibre2opds which builds a nice html interface accessible through the browser on your kindle.
If you don't use calibre, there is a script called pyndexer which indexes your library and provides you access through an ordinary html index.
This is the thread on how to set this tool up.
To answer the original question: unfortunately
the Kindle doesn't let you download PDF, MP3 etc. It's clearly done to minimizing the data volume. The
Kindle User's Guide states the only formats you can download through your browser:
Quote:
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The types of files you can download include Kindle content (.AZW, .AZW1), unprotected Mobipocket books (.MOBI, .PRC), and text files (.TXT)
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