The first problem you'd have is that chameleons are protected under the Convention on International Trade in Endangered Species (CITES). As a result, it is illegal to transport them across international boarders without CITES documents from the exporting country. That means every time you crossed into a new country, you would have to wait for a new permit from that country to be issued and you would need to have your chameleon and its paperwork inspected and approved. If you didn't, you'd be breaking the law and could go to prison.
Legality aside, many chameleons, including veiled chameleons, communicate using substrate vibrations so the constant vibrations from the car would be stressful, not to mention the moving traffic and swaying with turns. Also, how would you plan to monitor his temperatures, particularly when you are not in the car? Carrying the cham around with you so it doesn't bake in the car is also stressful.
Not a good idea.
Chris