[8.9" Kindle Fire HD Q&A, Help & Troubleshooting] monster1612:
Nothing changed. If you get the device to show up with the adb devices command, then everything's theoretically set up. The only reason you're getting an error with su not being found is that you aren't rooted. Here's a quick way to get root (like actually super simple, considering you already have ADB working):

1) download the attached 8.1.4 bootloader file (this is ripped straight from my Kindle before I "upgraded" to 8.5.1 to test this out). you may consider placing it in the same folder as the adb program. Also download SuperSU and the latest TWRP build for this device.

2) shut down the kindle and make sure it's plugged in.

3) run fastboot -i 0x1949 getvar product, then power the kindle on. when you see "fastboot mode" on the kindle, you should see something in the command prompt that begins with "Jem". if you do, then it's working. :)

4) type fastboot -i 0x1949 flash bootloader jem_8-1-4_bootloader.img to flash the 8.1.4 bootloader. this is ESSENTIAL because the kindle won't boot custom (unsigned) images otherwise. more explanation below...

5) next, type fastboot -i 0x1949 flash recovery twrp.img, where twrp.img is the file name of the TWRP image you downloaded earlier.

6) type fastboot -i 0x1949 oem recovery to kick the Kindle into recovery mode. if all goes well, you should see "TWRP" on your device after a few moments.

7) copy the SuperSU zip you downloaded to the kindle's internal storage. then on the kindle, tap Install. Next, on the side menu to the left, swipe up from the bottom and tap "sdcard" (referring to the internal storage that you see on the computer when the kindle's plugged in). Tap the SuperSU .zip, and then swipe where indicated. Feel free to reboot the system, and then voila, you're rooted. You should be able to run those backup commands. As a bonus, you won't have to download TWRP or the bootloader image from that virus-laden d-h.st site - avoid it like the plague.

8) Because TWRP's already flashed, you can type adb reboot recovery from the stock OS to begin flashing a new ROM right away.

A couple side notes...

1) Because you've flashed TWRP, a custom recovery, there is no need whatsoever to run the stock recovery backup command. It's already been overwritten, and if you really need it (which, again, is highly doubted because it only lets you run a factory reset), you can actually extract the recovery image from the system partition. Just run adb pull /system/recovery-prod.img stock-recovery.img instead of the adb shell su... stock-recovery.img one.

2) You have to flash the 8.1.4 bootloader because the one you currently have is more than likely a newer version. Custom ROMs (and even recoveries like TWRP) rely on an exploit in the 8.1.4 bootloader in order to trick the device into running the image (and newer bootloaders have this exploit patched already). So technically, because the exploit has to be run every time, the bootloader is never "unlocked" - merely tricked. Without the older bootloader in place, you get what is referred to as the "red screen of death". It's not pretty, but it's not permanent either. (Just power off the kindle, and then run the fastboot command involving "getvar product" to get it to the bootloader so you can flash the 8.1.4 bootloader and go forward.)

Hope this helps!