To answer your question, I can say that my daughter and SIL took 6 of my best laying hens from Oregon to Tennessee in the back of a small trailer, pulled behind their truck, that had a wired gate enclosure (about 10? years ago). The hens did fine. Place some apple slices for nourishment and moisture for them. They even got a few eggs on the way (it took about 4 or 5 days?). Other proof that chickens move just fine, my grandparents traveled from South Dakota to Oklahoma in the 30's in Conestoga wagons after the farm failed with the dust bowl. They placed a flock of chickens in the wagon tail gate, let them out to forage in the evening, to roost on the axles, then put them back into the tail gate as they traveled. They got a few eggs along the way.
Having said all THAT (you will successfully, easily move them), be prepared in these days of Avian Influenza that the locals probably won't appreciate you're moving said hens. Many on this list will have a strong opinion that you should sell said birds and simply get new ones to avoid cross contaminating the population, or at the very least clearance from a vet.
Simple answer, have a small enclosure, hay bedding on the floor, secure sides, top, gate, they'll be fine. Complex answer is it may be a poor idea depending upon your AI exposure.
LofMc