In order to add Dropbox to Twine you need to create an app in your dropbox account that allows Twine to access your files. To do this go to this URL:
Once you're here, enter the settings shown in the screenshot below:
Once you agree and submit the app you'll be taken to the next screen. Please add all the settings and most importantly add a Chooser / Embedder domain of 'twineapp.com'.
Click on 'Apply for Production' in the top right of this screen. Then copy the 'App Key. and send to your account manager for them to enable and check your settings within Twine.