Amazon updated the Kindle Fire to version 6.2.1 in an effort to stop users from rooting the device but root access is back. This update to 6.2.1 took root access away from user along with blocking the ability to re-root the way it was done previously. Root access is again available for the Kindle Fire now on version 6.2.1.
Type “adb shell chown 0.0 /system/xbin/su”, press enter
Type “adb shell chmod 06755 /system/xbin/su”, press enter
Type “adb install com.noshufu.android.su-1.apk”, press enter
Type “adb reboot”, press enter
Congrats your Kindle Fire is now rooted running version 6.2.1 and below. If you run into any issues drop us a line and there is also more information at Rootzwiki. The people that get the credit for the above method are … Justin Case (case), Vashypooh, Trevor Eckhart, IOMoster , AndroidPolice.com, RootzWiki.com, and ChainsDD.