If you manage to change your password on the Fire, your email won't work on your other devices.
Are you absolutely sure you have entered the password absolutely correctly, they know the difference between capital and lower case and a space is part of a password. When you enter a password, there is usually a little symbol at the end of the line, sometimes looks like a closed eye, if you select that, you can see what you typed and check for mistakes.
If you get locked out, you will have to reset your password on all your other devices too. Let us know what happens.