This post originally used Zergrush to root, but that no longer works with the latest updated software from Amazon. Check the development section to find the latest rooting information.
1. Root your Kindle Fire.
2. Obtain/install ADB, sqlite3, and the KF USB drivers. Make sure the KF shows up when you execute the command "adb devices" from a terminal.
3. Execute the following in a terminal window:
adb pull /data/data/com.android.providers.settings/databases/settings.db copy settings.db settings.bak sqlite3 settings.db "update secure set value=1 where name='mock_location';" adb push settings.db /data/data/com.android.providers.settings/databases/settings.db adb reboot
Alternative Method: Purchase Root Explorer from the Play Store on your rooted KF. Use Root Explorer and sqlite editor to open /data/data/com.android.providers.settings/databases/settings.db and change 'mock_location' from '0' to '1'. Restart your KF.
Thanks goes to ros87 for posting this method for the Nook Touch here.