There are no native email commands in AGK. I also don't think there are any raw TCP functions (which would...I guess allow for a pure AppGameKit implementation)
I think the easiest way would be some kind of HTTP interface (on an external server), with AppGameKit using it's native HTTP functions.
[href=https://www.appgamekit.com/documentation/Reference/HTTP.htm]https://www.appgamekit.com/documentation/Reference/HTTP.htm
[/href]
I know GMAIL can use IMAP or POP3, so any standard PHP email function should be able to retrieve it. I don't use iCloud, but assume that can also provide IMAP and/or POP3 to the mailbox.
You'll need to create some PHP scripts to output the email data. Possibly 1 script to list just the emails (with message ID) and another to retrieve the full message (you provide the ID)
If you use the GetHTTPResponse command, the PHP script will not need to save files, if can just echo to the browser (and GetHTTPResponse can grab that).
Security will need to be good, but I guess you only need read-only, however the senders name and email would be visible so you would certainly need to restrict access (.htaccess and .htpasswd on the web server would be a good start, but also ensuring your running on SSL).
Check out the SetHTTPHost command, it allows username+password to be sent.
If you do have an SSL link, you could even pass the pop3 host, username and password to the PHP script.
It'll be clunky, and I'd think about why you need this.
This would be no good for a AppGameKit email client. ... just in case that is your plan.
