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.
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!