There is an Android app for the Kindle Fire to use the TOR network. I stole this from the following website:
1) Under the settings section labeled “Device,” there is an option that says “Allow Installation of Applications From Unknown Sources.” Enable this!
2) Then download these files directly via the Fire’s browser, or side-load them from the desktop using the Android SDK “adb” tool.
3) Start Orbot, follow the wizard, and press the power up button to connect to Tor.
4) Start Orweb to connect to the Tor Check page to verify your connection, then browse away to your (private) heart’s content.
5) Do a happy dance because your Kindle Fire just got way more l33t and slightly less p0wn3d.