To login to iCloud from BlueMail, you need to use your Apple ID email address, e.g. user@me.com or user@icloud.com or whichever mail was granted to you by Apple.
You should not use any connected mail address like you can for web, as BlueMail needs your Apple mail credentials to connect to your mail using IMAP.
You can add a new iCloud Account using: Settings | Account Settings | Add Account | Manual Setup | iCloud.
iCloud users (@icloud.com, @me.com, or @mac.com) have to generate an app-specific password to sign into their accounts on email clients.
How Do I Enable an App-Specific Password for my iCloud Account within BlueMail
You will need to do it inside the settings of your iCloud account, please also see: Steps from Apple to enable app-specific password
