To login to iCloud from TypeApp, 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 TypeApp needs your Apple mail credentials to connect to your mail using IMAP.
You can add a new iCloud Account using: More (o o o) | Various Account Settings | Add Account | iCloud