First note that the car is rough cut previous to this operation. Trying to do this operation as if one is slicing the car "in half" is not a good approach with a mill. You will note that I have said this previously, so it is not a surprise.
I place the car (part) with the opening (floor) downwards, with the car parallel to the table. It could as well be placed with the opening upwards. It really doesn't matter, except the details of the clamping.
Such a car would be clamped by two bars crossing perpendicular to the long axis of the car. The bars are secured by screws down to the table. Some auxiliary shim-like pieces have to be installed so that the load goes down through the sides, rather than through the center of the roof.
There are risers under the work for clearance of any tabs or steps, and to allow cutter clearance.
The path I take is such that the cutter goes from back to front and makes a cut. It is then lowered and repeated. Keep in mind that the cutter is trimming the rough cut. It is not making the original cut.
As I said, I use an internal block. Properly installed, the sides will not do any flapping.