Afaik, the current whisper system has never been offically released for developers hence there’s no official documentation.
The main area of application is Twitch.tv and it’s working perfectly fine there.
This is pretty much how you send a whisper if you’re connected to the group chat server except with some small changes. Here’s the raw message:
privmsg #channel .w recipient your message here
In this case, #channel can be any valid channel since whispers are channel unrelated