Hi Essie1956,
Welcome to Apple Support Communities. I understand that you're having trouble using your @me.com email address to sign in to an email app on your Kindle Fire because the password isn't recognized. I can see why you'd reach out about this; I'd like to help. You are correct that the password to your @me.com address should be the same as the Apple ID password you use in the iTunes & App Store, but because you're signing in to a third-party email client on the Kindle Fire, you'll need to use an "app-specific password" in order to complete the set up: Using app-specific passwords
In order to use an app-specific password, you'll need to set up two-factor authentication security on your Apple ID: Two-factor authentication for Apple ID
If you happen to need server settings for iCloud email on the app you're using once you've signed in with your app-specific password, this resource will help: Mail server settings for iCloud email clients
Best Regards.