I don't know for sure, but I think there was extrememly limited production of a few cars during the war...they went to the government, for such things as staff cars. I guess it's possible a few made it back into civilian hands as surplus.
There were V-12 flathead Lincolns in the 40s, and a very few straight 8 Chrysler flatheads.
I had an elderly neighbor when I was growing up in the 70s. He had an Edsel that they drove to town, and a 50 Buick with a straight 8 that he used as a pickup (he removed the back seat).
I always thought the Buick was a flathead, but the Internet tells me it was OHV.