Just wanted to say that I am having SAME Problem, tried lots of fixes with adb and powered off cable and USB to Ethernet but it gives me no chance to allow debugging. I am going to click on above link for Fire TV Customer Support.
I had the same problem with my Fire TV 4K (The square one with the attached hdmi cable), but only if I had a USB hub connected to it. My solution was using a higher powered USB power supply for the hub. The Fire TV worked fine with a 1 Amp PSU, but went into the loop once I put the hub in the mix. Replacing the USB power supply with a 2 Amp unit solved my issue.
Hello, I had the same problem. I did not have my fire stick 4k connected to my laptop adb before I installed Google play so I could not uninstall play store and play services using adb. I came across this link and followed exactly what mentioned, It let me boot in to safe mode then I uninstalled play store and play services then did a normal boot. It works well now. (This url is non-English so allow google translate to English) I got y-otg cable from Amazon, I Kept holding ctrl+alt+menu+printscreen keys while another person assisted to plug in the fire stick power adapter. I kept hitting the "i" key. It started the regular white screen with orange amazon logo after few moments darkscreen+safemode in left bottom appeared then I got my screen. clicked "your applications" and uninstalled both culprits then power off and power on. (Both blue tooth and usb key board supports to invoke the safe mode)