Less than a month after hackers figured out how to unlock the bootloader and root the 8th-gen Amazon Fire HD 8 tablet (the 2018 model), there’s now a method for doing that with Amazon’s cheaper 7 inch tablets.
Xda-developers forum member k4y0z has posted instructions for unlocking the 5th-gen and 7th-gen Amazon Fire tablets (the versions released in 2015 and 2017).

You should read all the instructions before you get started to see if you’re comfortable with the whole process. For example, if you have the 2017 version of Amazon’s 7 inch tablet, there’s a chance you may have to open the case and use a paperclip or some other conductive item to short a circuit — although some folks have been able to unlock the 2017 model without taking that step.
If you have a 2015 model, you don’t even need to open the tablet up. All you need is a micro USB cable and a computer running Linux.
But either way, there’s a chance you could at least temporarily brick you tablet if something goes wrong.
The good news is that if you break your tablet you probably won’t be out a lot of money — the Amazon Fire 7 has a list price of $50, and this week it’s on sale for just $40.
Anyway, once your bootloader is unlocked, you can install a version of TWRP that lets you load custom firmware onto the tablet. This makes it possible to root the 5th-gen and 7th-gen Amazon Fire tablets, remove pre-installed software you may not want to use, or even install custom ROMs.

While the Amazon Fire isn’t exactly the best tablet money can buy, it is certainly one of the best cheap tablets. It has a 1.3 GHz quad-core MediaTek processor, a 7 inch, 1024 x 600 pixel IPS display, 1GB of RAM, and 8GB to 16GB of built-in storage plus a microSD card reader and 3.5mm headphone jack. There are front-and rear cameras, and support for Bluetooth and dual-band WiFi.