US Army field kitchens were most likely in the back of 2 1/2 ton trucks. I have a copy of a government publication which shows all vehicles used by the US during WW2 and there are no field kitchen trailers listed (as of 1943) so they were likely field built or modified as field expedients.
Interesting that the Brits, Russians and Germans had field kitchens trailers, but the US relied on C and K rations to feed the troops in the field. The USA had kitchens that set up in the rear echelon areas and they would occasionally send hot meals up to the front using thermal carriers.
Now, today’s Army does have mobile field kitchens. I don’t know how they utilize them though...