Different devices don't learn passwords from each other. Your email sever needs a single ID (your email address) and a password to access it. So you will enter the same password on each device, the device then sends that password to the server which allows you read your emails.
It may be that your password on your Kindle may have been corrupted somehow and now you don't know how to add it back so the Kindle can show you your emails. It sounds as if you have forgotten your password (it must be exact, upper and lower case letters are different).
However, your phone still holds the current email password in its memory. If you change your password on the hotmail account, you will have to put the new password on any devices you use to access it.
You could try resetting your password using your mobile phone to read the reset link. You will have to log on to your Hotmail account, giving your email address but when Hotmail ask for your password, click on the forgotten password link. If you are lucky, you may get an email on your mobile phone allowing you to reset your password.
If you can reset your password, you will need to re-add it to your Kindle and mobile phone. Some email providers ask you for a recovery email. It may be worth considering getting another email address with a different provider for this purpose.
You have to remember that there is a lot of information in your emails. It is important to take security seriously, passwords are so important.