Will it damage any part of a honda civic 2014 to do this?

Put on jack stands take off wheels put the car in drive and run it until it has 150 miles of wheel spin in the air? Don't ask why its complicated. Ill turn off traction control

No, it will be the easiest 150 miles its ever had beause with the wheels off the ground its not being put under any stress from wind resistance tire rolling resistance ect

A tried-and-true method of doing this is to leave the wheels on and not use the jack stands. If you start the car and put in in drive, the wheels will actually spin just like that. Note that the car will become in a state of motion. Steer by turning the wheel. Use the two pedals to speed up and slow down. Obey all traffic laws.

Continue until 150miles has been achieved.

Good luck keeping the RPMS low why would you take the wheels off

We do this all the time on the 2 post hydraulic car lift. We leave the wheel on We just leave it in Drive or 1st gear without pressing the gas pedal. Same concept if you put jack stands. I would use (4) jack stands to even out the vehicle.

A twisted mind is a complicated thing.There's no reason in the world to try and put 150 miles on a vehicle in the air.

Nothing is complicated about a low IQ

I see no reason to do it, but it wouldn't hurt the car.

Yes. Without the wheels on to tightly sandwich the brake rotors against the the wheel bearing flange, the rotors will be loose and you may damage the wheel studs and elongate the stud holes on the rotors.
A safe way to do this would be to go to a hardware store and buy 12 hex nuts that will slide over 3 wheel studs on wheel flange with the rotors in place *then snug-up 3 lug-nuts over the hex nuts to hold the rotors firmly in place on each wheel.

Consider how long it will take - the same as driving 150 miles at whatever engine speed (top gear, I presume) you have in mind. Two hours at 75 mph (not recommended), three hours at 50 mph…

No, it won't hurt it, but you will get some drive train flags for no load on the engine and probably an ABS light for the rear wheels not spinning after less then a mile. Yeah, maybe to test it that way quickly to make sure the repair of the spinning wheel drive components are good and noise free, but 150 miles worth is total Ferris Bueller style ludicrous.

You should never do this unless you are jack standing the vehicle by the lower A frames, doing it at full suspension travel will damage the CV/U joints. Jacking it up front only on stands under the lower suspension is OK for a quick spin and noise test. The CV/U joints are not designed to operate at a constant fully dropped airborne suspension position.