The Flexpreis ticket allows you to interrupt the trip and does not require you to take specific trains. So what you can do is to use the ticket to take the subway from STR to Stuttgart main train station (Hauptbahnhof, HBf). You can then interrupt your trip there, buy a VVS-ticket to go to the Mercedes-Benz museum and back to Stuttgart HBf, and then resume your travel on the Flexpreis to go to Mannheim.
The Flexpreis will include the city option for public transport, but this option is only valid on public transport from your arrival point to the nearest train station and from the train station to your final destination. People have used the City option for detours, but in the case of a visit to the Mercedes-Benz museum it is fairly obvious that you're violating the conditions of the ticket (it is on the other side of the HBf, as seen from the airport, so there's no way you can claim that you're on your way to the HBf). Given that the one way ticket from the HBf to the museum costs only 2.50 EUR, I would not take the risk.