We have been on the road almost 10 years now. Walmart and Safeway have been our pharmacies of choice, although now in Texas, HEB is filling in nicely. You just do what you do at home, have your doctor fax the order to the nearest pharmacy you want, or have it transferred pharmacy to pharmacy.
The only problem we ever faced was having a refill in NY. It seems that when we left the state, our refills on record did not travel with us, the doctor had to re-fax the order to the next location.
Also, we learned that my wife's test strips for diabetes, needs to have a new order faxed to each pharmacy, as the codes do not properly travel pharmacy to pharmacy. A little inconvient, but never slows our travels down a bit.