The blue tool is an “iFixit Opening Tool.” There is a link to it above the video, in the “Tools” section of this page. And a link to the Charging Assembly is listed above, in “Parts.”
I purchased this tool directly from iFixit. I'm happy with it, although there may be other good brands. There are links above to buy the tools (next to the little blue shopping cart icons.)
I hope this helps you, and good luck!
I'm sorry I took so long to respond. I don't have personal experience with the HDX, but here's a link to instructions someone else made on iFixit: Kindle Fire HDX 7" USB Charging Port Replacement
Also, here's a quick video review for an HDX teardown, to give you an idea of the level of whether you feel up to the task: Kindle Fire HDX 7" Teardown
It looks to be more difficult than the regular HD 7. On the plus side though, it seems the USB Charging port is a plug-in component, which does not require soldering to replace. That's a good thing always. I hope this helps you.