Do you have https://gist.github.com/4034526 working already?
http://omz-forums.appspot.com/pythonista/post/6675908186341376
Once dropboxlogin is working, you can:
Use https://www.dropbox.com/developers/core/docs/python#DropboxClient.get_file
with client.get_file('/magnum-opus.txt') as in_file: the_data = in_file.read()