Reporting back on this. We are flat towing our 2016 MKX without any problems. We had to convince the Dealer it would work. The dealer said it wouldn't but we got the Sales Manager to call Lincoln and tech support told them it did indeed work fine.
It is detailed in the owners manual and works fine.
You turn on the car without starting it then go into Settings > Vehicle > Neutral Tow Mode and hold down the OK button. Then with your foot on the brake tap N on the gear selector. The car's display reads Neutral Tow Mode Engaged. Then you turn off the car. Done.
Tows great.
Be aware that only BlueOx makes a baseplate for the 2016 MKX but only for cars without Adaptive Cruise Control.
We love our MKX and love taking it on trips with the RV.
PS. They stipulate 65mph only. And running the engine before towing every day and every 600 mi during the day.