I had the same issue last month when I couldn't remember my Kindle password. I found the password reset option by going to the Amazon website and logging into my account. Once logged in, I clicked on 'Account & Lists' at the top right corner, then selected 'Login & security.' From there, I clicked on 'Edit' next to the password section and followed the prompts to reset it. It was pretty straightforward, and I got a confirmation email right after. If you're using the Kindle app, you might need to log out and log back in with the new password.
Another way is to use the 'Forgot your password?' link on the Kindle login screen. This will redirect you to Amazon's password reset page. Just enter your email or phone number associated with your account, and they'll send you a link to create a new password. Make sure to check your spam folder if you don't see the email right away. I’ve done this a couple of times, and it always works like a charm.