Firerooter is a tool that makes it easy to perform administrative tasks on your Kindle Fire HD 7" 2013 (KFSOWI/Soho), such as reinstalling the system or rooting the device, as long as you have a fastboot cable. It does not work on any other devices, and may permanently damage them.
You can download Firerooter for your OS of choice or you can get the code from GitHub.
Easy! Just turn off your tablet, connect it to your computer with your fastboot cable and press Install and modify FireOS. You'll be able to root your tablet from there.
If the program isn't working properly, make sure you are connected via a wired Internet connection.
You may also want to disable any antivirus software, especially if you are getting an error message of the form "file downloads/<some filename> not found". Firerooter is open source software, so you can always check the source code if you don't trust it.
Every now and then I like to push out updates to Firerooter to add new features or fix bugs. You probably want to download the latest version (the older ones are even buggier!)
Here's a list of updates I've released and their changelogs:
0.3-devel
0.2.3-devel
0.2.2-devel
0.2.1-devel
0.2-devel
0.1.1-devel
0.1-devel
You can help me work on Firerooter by submitting pull requests on GitHub. If you do submit anything, please make sure it has been tested and that it works reliably.
If you run into any issues or want to say thanks or need help or whatever, feel free to email me! Please do your own personal research before emailing me, i.e. if you're emailing me to ask something and the answer is readily available on the Internet, I will not answer your question.