SFAIK a suspended tow is OK ie the driven wheels off the ground and not turning. Anything else and there are speed and distance limits and I had one car where the handbook mentioned adding extra ATF fluid to the box. So, a flat loader or a suspended tow is the best way forward. What does the car handbook say?
My Peugeot hand book says, if you are towing with all 4 wheels on the ground, Gear box in 'N', less than 50 mph, not more than 30 miles and do not add oil to the box.
Vehicles with automatic transmission should be towed facing forwards only and must not be towed faster than 50 mph (80 km/h) or further than 60 miles (100 km). If the transmission is defective, or if the above speed or distance is to be exceeded, the front axle must be raised off the ground.
To prevent the entry of exhaust fumes from the towing vehicle, switch on the air recirculation (if fitted) and close the windows.