Do this at your own risk. This could be a dangerous procedure, and I am not responsible for any possible damages. Be smart, guys. :)
First, download the Kindle Fire HD 7″ drivers from here.
Download the necessary files from here. Unzip them. Take su from /system/bin/ and Superuser.apk from /system/app/ and put them into your current directory.
From command prompt, run:
adb shell
rm /data/local/tmp
ln -s /data/ /data/local/tmp
exit
adb reboot
adb shell
echo ‘ro.kernel.qemu=1′ > /data/local.prop
exit
adb reboot
adb shell mount -o remount,rw /system
adb push su /system/xbin/su
adb shell
chown 0.0 /system/xbin/su
chmod 06755 /system/xbin/su
rm /data/local.prop
exit
adb reboot
adb install Superuser.apk
You should now be rooted!
SOURCES:
XDA-Developers | RootzWiki | Android Police