I believe you might be going about it the wrong way. Try these steps and let me know if you still run into any issues!
1. After flying your first flight, exit to the main menu. (I recommend saving your flight before continuing, just incase!)
2. Press the 'Simulation (S)' tab on the top toolbar.
3. This will then prompt you with an aircraft screen. Select the aircraft you'd like for your next flight.
4. Select spawn location. You must choose a different location than the previous flight(s).
5. Fly your next flight.
6. Repeat the process for any additional aircraft.