Updated with instructions to install gadget
Step 1: Go to GMail Labs and enable Add Gadget by URL feature
Step 3: Add the Greasemonkey script for Dropbox mobile:
Step 1: Go to GMail Labs and enable Add Gadget by URL feature
The gadget URL is: http://files.dropbox.com/u/232/gadgets/dropbox_redir_mf-v2.xml
After receiving a request from a user for creating a dropbox gadget for Gmail, I went ahead and made a User Script that modifies the Dropbox Gadget UI for use in Gmail. I could not rework the UI remotely, so the script was the only practical choice.
I have tested it and it works both in Firefox and Google Chrome.
Enjoy.