How to move my iCloud self generated mailboxes to Mail on my Mac?

If you are referring to mailboxes that you create under the Folders heading in iCloud, then these should show up in the Mail app on your Mac if you are logged in with the same Apple ID.

They would appear under iCloud in the left-side window of the Mail app. In the example below, I only have to named folders under Folders in iCloud Mail, Deleted Items and Sent Items. Here they are in the Mail app on my Mac mini.

For each email account that you set up in the Mail app, the app will create a link to it any any folders that email account uses. I provided you an example from my iCloud email account. You don't directly create these, they are created when the Mail app successfully links to any email account. For example, what you would see for a Gmail account would be different than what you would see for Outlook, Yahoo, etc. Basically the only email mailboxes that would be common would be things like the Inbox, Sent, Junk, & Trash.

So, depending on which email account you are having issues with, I would suggest that you remove, and then, re-add it back to the Mail app and let the app "rebuild" the mailbox folders that it finds associated to that account.