how far are you moving them? Time not distance. Will you be moving them at highway speeds?
Is their new home ready for them to take immediate occupancy? This is critical, no matter what or how they are moved. It is very stressful riding in a vehicle and going somewhere strange for humans, and for chickens it can kill them.
The suggestion to move them at night is great! If it is a short local move I suggest renting or borrowing a panel van and getting 2 appliance boxes that will fit on their sides inside the van. Make lots of holes in the "top" for ventilation, and cut the real top so it flaps down out the back door of the van. Put a couple inches of bedding in the boxes, place no food or water have that in place in the new home. Gather the sleeping birds and put them in the boxes, tape the lid securely and drive directly to new home. When arriving home unload as quietly and peacefully as possible to avoid hysterical hens. Work in the dark or as dark as feasible so they think it is sleep time. Keeping themin the boxes will make clean up for the van pretty easy. This is a matter where your sanity needs to be weighed against monetary savings.
Moving them inside the car will one, ruin the car, they will poop excessively due to stress, claws can rip up the interior and they will panic and you could have a cyclone of flying chickens while you try to drive. Even with ear plugs the noise level will probably be painful, literally.
I drove from OH to NM with the backseat of my Galant made into a cat kennel, and for 4 days 4 cats screamed every one of 2000+ miles. I thought I was ready for commitment when we got to the new house.