Hi there, @GbmView,
To shed some light with your question, there isn't a direct way to sync or transfer mileage from QuickBooks Online to QuickBooks Self-Employed. They are a totally different platforms and are using separate databases and programming.
You will need to manually record the data in your Self-Employed account to match the data with QBO. Go to the Miles menu and select Add Trip to start tracking mileage.
Also, QuickBooks Self-Employed has the automatic mileage tracking where users can now utilize their mobile devices to track trips. See this article for more details: Use automatic mileage tracking for QuickBooks Self-Employed.
I'm also enclosing here another resource link where you can find helpful articles about mileage and how it works: Mileage tracking in QuickBooks Self-Employed.
Having the option to integrate data between QBO and QBSE is a great idea. This way we can keep your records accurate in both profiles. I'll be sending a product request to our engineers letting them know you want this preference.
If you have additional question with anything in QuickBooks, mention me anytime. I'm always here to help you. Have a wonderful week ahead!