Here's a copy of a post from another site in which the user successfully registered a Kindle Keyboard 3rd gen. Hope it helps someone.
1) to register
https://www.amazon.com/gp/help/custo...deId=201819620
2) check for the latest s/w version:
https://www.amazon.com/gp/help/custo...MQC26VQQMM8XSW (hopefully that link will stay ok),
3) to manually update your s/w
https://www.amazon.com/gp/help/custo...AE5G5UGCYA25DW
4) if you have problems with the login read this:
https://www.amazonforum.com/s/question/ ... e-keyboard
5) the hitch with the login and OTP (which I just tried on a lark because it occurred to me that I never did actively enable 2 step verification)... even if you have not enabled 2 step verification on your account, you will likely be sent an OTP. But it won't work to register your device until you enable 2 step verification.on your account. Stupid right? Cuz it does work when logging in on the web. Did the Customer service guy help? no. Claimed that there was a hardware fault, or that the Kindle Keyboard 3rd gen was no longer supported. 'tis a lie. So...
TLDR: Just enable 2 step verification on your account and then when the kindle says it can't find and account associated with your email & <yourpassword> - you'll get an OTP (in whatever method you've set up) then (at least for me) enter <yourpassword>OTP (i.e if your password is ThisIsAP@1n! and the OTP sent is 123456 then enter ThisIsAP@1n!123456 in the password field. If that fails try just the OTP code in the password field.