The Kindle Fire 7-inch (thor) and 8.9-inch (apollo) HDX tablets have had Safestrap and custom ROM support since January 2014, but now they both have a custom TWRP recovery. A recent discovery by XDA Forums member @vortox means that both of these HDX tablets can be unlocked, opening up access for customer recoveries. This brings TWRP 18.104.22.168 to these tablets. The process is risky and could leave you with a bricked tablet, but that's almost always the case when you start tinkering with bootloaders and custom ROMs. Proceed at your own risk.
The 7-inch Kindle Fire HDX (thor) recovery can be found here. You'll need to download the recovery image and then use an application like Flashify to flash the custom recovery. You will need to be rooted already, and be running HDX firmware 22.214.171.124. If you have an 8.9-inch Kindle Fire HDX (apollo), the process is a little bit different. You'll need to be rooted and have the same 126.96.36.199 firmware installed, but to install the custom TWRP recovery you'll have to work some ADB magic. Download the recovery image and put it on the root of your SD card, then ADB into your tablet and run a few commands to install the recovery. You can find the 8.9-inch HDX TWRP recovery thread here.
Both of these tablets got Safestrap and custom ROM support back in January of 2014, but that method merely bypassed the bootloader. Until the bootloader was unlocked the recovery couldn't be changed. Safestrap installs a separate bootloader and bypasses the locked bootloader on the device. This is a relatively safe method to use, but it's easier if you can just install a custom recovery and avoid having to use the workaround. Now that the Kindle Fire HDX's bootloader has been unlocked, this has all opened up for more and better development. If you own a Kindle Fire HDX and are a fan of modding your tablet, XDA developers have come to your rescue again. Click the source link below to head on over to the XDA Kindle Fire HDX development thread to find these TWRP recoveries and everything else that you'll need.