How can I get Outlook to stop asking for a Keychain login if I don't want to use keychain?
Keychain as you may be aware by now is the main system OSX uses to store your passwords. Anything you ask to be stored is sent to the keychain. Therefore if you choose not to save any passwords you will be asked to enter the password in every time it is required, which is what the keychain is designed to do.

If you do not want to save passwords to the keychain, then no you cannot get around the keychain pop up question.