If the Kindle has a proper email application you should be able to set it up using the settings listed here:
The Kindle will need to be able to handle IMAP and SSL. You will not be able to set up any of iCloud's other facilities.
Doesn't seem to do the trick. This is a brand new kindle fire hd delivered yesterday. The setup procedure does not ask me about SMTP Authentication. Instead, it asks me to select the security type from a list of five options: none, SSL/TLS, SSL/TLS (accept all certificates), STARTTLS or STARTTLS (accept all certificates). I selected SSL/TLS (accept all certificates) because it is the only option that actually processes before giving me the error message!