This can be achieved with the first car given to you but will be easier with the faster and more agile cars
There are many jumps all over the Paradise world but there are two locations in the game that this is easiest as it has the largest jumps. The two areas are the Quarry and the near by South Mountain Drive jump.
To initiate a flat spin you need to spin off of a jump so that the car spins sideways in the air. The best way to do this is to hold the handbrake (Press
) whilst turning just as you are about to launch off of a ramp.The 360 has to be in the air so any spinning done on the ground wont count
Here's a video demonstrating the South Mountain Drive jump, however the Quarry can be seen at 1:02 on the left.