Technically you can screw it on the instead of the fixed sprocket, however it's not the best as it sits on half of the thread than it is supposed to sit because the counter thread takes up the rest on the hub. Do you not have a flip flop hub?
Unless I'm mistaken, a 'flip flop hub' does not necessarily mean one side is meant for a freewheel, no? You can have flip flop hubs with the situation you described on both sides. The DT Swiss 370 track hub, for example.
Technically you can screw it on the instead of the fixed sprocket, however it's not the best as it sits on half of the thread than it is supposed to sit because the counter thread takes up the rest on the hub. Do you not have a flip flop hub?