I have an Azure Managed Instance and a database that I am able to connect from SSMS and Power BI Desktop, port 3342, but I am not able to schedule a refresh from within the Power BI Service or MS Flow. My guess is that there Azure to Power BI ports in use but not configured in the Network security groups?
Update - I was able to use PowerShell's PBI module's REST method to trigger the dataset refreshes.
Since SQL MI is within a Vnet, you would need a On premise gateway for schedule refresh to PowerBI report service from SQL MI.