[Fire HD 6 and 7 General] DoLooper:
TWRP (Team Win Recovery Project) replaces a device's stock recovery and provides, among other options, the ability to install img (image) and zip files. TWRP for the Fire HDs was developed by JMZ and is described here.

How to install TWRP

These steps are for a first-time install on a rooted Fire HD running OS 4.5.3 with stock bootloader and recovery.

At this time, 4.5.3 bootloader is required. You're welcome to try to get it onto a different OS, but you need the 4.5.3 bootloaders and I'm not getting into that. So, if you're running a different OS, have messed with partitions or done something that requires a TWRP reinstall (other than reinstalling 4.5.3 and rerooting), you risk being unable to boot recovery or bootloop/brick.

OK, that doesn't sound so "newbie-friendly" :) but this really is a simple process that should always go smoothly on a "clean" OS 4.5.3.​

You can easily install TWRP with either TWRP Manager (also by JMZ) or Flashify from the Play Store.

If you don't have Play Store access:

- Flashify - v 1.9.1 from APKMirror

- TWRP Manager - Download from JMZSoftware​

For installing TWRP, the only difference between the two is that TWRP Manager auto-downloads the correct TWRP version while Flashify requires you download it yourself.

[EDIT 8/16/2015] At this time, TWRP Manager doesn't seem to be working. Use Flashify, instructions below. Steps for TWRP Manager are at bottom of post.

Install TWRP with Flashify

Download JMZ's ariel TWRP image (https://www.androidfilehost.com/?fid=24052804347756852) to the Fire's download folder.

Install and run Flashify (download link above) and give it superuser access when prompted. It probably will also prompt to apply loki patch for Kitkat. Say yes.

Tap Recovery Image and then Choose a File.

Navigate to download folder, tap the TWRP file, and when Flashify asks if you are sure, tap Yup!

If install succeeds ("Flash Complete"): (a) Tap Reboot now. (b) When back in Fire OS, boot to recovery (below) and confirm you're in TWRP. Note: If tablet bootloops, post the problem in one of the bootloop threads.

If install fails (error messages displayed), first take a screenshot. If you can determine the problem, fix it and try again or try TWRP Manager. If you don't understand the error or can't resolve it, post in a "TWRP install failure" thread.

How to Boot to Recovery

Manual: (a) Power off tablet. (b) Hold down power and volume-up buttons at same time until you see "Amazon," then release. (If you just boot back into Fire, you didn't power off first or didn't hold buttons long enough.)

adb command from computer: adb reboot recovery

- If you see TWRP, great! Check it out and then press Reboot and System to go back to OS.

- If you get stock recovery screen ("reboot" and "factory reset"), TWRP didn't install. Reboot should be highlighted. (If it's not, use volume-up or -down to select it.) Press the power button to click reboot and when back in Fire OS, try the other app.

[EDIT 1] For simplicity, install TWRP Manager on the Fire and follow these steps.

Install TWRP with TWRP Manager

Install and run TWRP Manager and give it superuser access when prompted. It will also prompt to apply patch for Kitkat. Say yes.

Tap top-left of screen for slide-out menu and select Install TWRP.

Confirm Device Name shows "ariel" and then tap Install Recovery. [download begins]

At warning screen, tap yes.

If install succeeds ("Flash Successful"): (a) Go to slide-out menu and choose Reboot Options and then Reboot Device. (b) When back in Fire OS, boot to recovery (above) and confirm you're in TWRP.

Note: If tablet bootloops, post the problem in one of the bootloop threads.

If install fails (error messages displayed), take a screenshot in case you need to post the problem and then look at comments here for a solution. If you can determine the problem, fix it and try again or try Flashify. If you don't understand the error or can't resolve it, post in a "TWRP install failure" thread.