You will have to revoke the application specific password which you had probably setup for your Kindle. Then reauthorize the device with username, password like earlier.
Here is Google's support document on turning off two-factor authentication.
Edit: I misread your question and provided the answer which works when you have 2fA enabled!
My earlier answer:
You will have to generate application specific passwords to do that. These are different from your Google Account password and are different for different devices/applications. Follow Google's instructions given here to generate the password(s).