Dropbox files viewer is the best app for managing/downloading your Dropbox files, designed from ground up for Kindle Fire only.
This app has been the Best Seller for productivity apps on amazon. Among top 50 paid apps on amazon appstore.
This is the best client for Dropbox on kindle fire. Works just like the official app of Dropbox.

Just login your Dropbox account, you will see all your files right away, all well sorted. Your folders,Starred,Recent,Shared with etc.
You can download any number of files for offline viewing, and even open with third party apps like Quick Office.
This is a super fast native app, not web app.Read your docs or flip through your albums when you're out and about.
Dropbox and the Dropbox logo are trademarks of Dropbox, Inc.
"Dropbox Client for kindle fire" is not affiliated with or otherwise sponsored by Dropbox, Inc.