Everyone with a rooted Fire TV or Fire TV Stick are now able to update to software version 184.108.40.206, thanks to Rbox who has just released pre-rooted ROMs of the new software version. As always, these ROMs are identical to the updates that Amazon released, but will allow you to update your rooted devices without losing root access.
You can find the download links to these new ROMs at the top of the following XDA Forum threads: Fire TV 1, Fire TV 2, and Fire TV Stick 1. Please be sure to donate to Rbox to support him and thank him for continuing to keep all of our rooted devices updated.
Use TWRP custom recovery, by following this guide, to install these ROMs on your rooted device. Fire TV Stick 1 owners may need to refer to this guide to be reminded how to get into and control TWRP using a PC.
As always, these ROMs cannot be used to root your device. Your device must already be rooted to install these ROMs. To see if your device’s software version is rootable and how to root it, see my guide here. Only the Fire TV 1, Fire TV 2, and Fire TV Stick 1 can be rooted if they’re running specific software versions.