You could really use almost anything to wind the line onto, but I've found that making cards like the one on the left is quite quick and easy. They could be made from thick card, hardboard or thin plywood. I cut them in a stack of 6 at a time in hardboard using an electric jigsaw - very fast...
Dimensions are not really important here, I made mine about 10cm x 6cm.
Either tie one end of the flying line around the cut-out part, or use reinforced tape to stick one end of the line to the car (quicker but not as safe!)