STILL NEED a Halloween costume? Go to a Goodwill, buy a trench coat and suddenly you’re Humphrey Bogart, brooding in the fog at the close of “Casablanca.” Whenever vintage purveyor Brian Davis comes across an antique trench while purchasing for his Brooklyn shop, Wooden Sleepers, he said he thinks of such Hollywood clichés. The archetypal khaki cotton trench, popularized by stalwart British brands like Burberry, is baggy enough to add 10 pounds, with large lapels, epaulets, two rows of prominent buttons and a belt tethered around the waist. Mr. Davis does not stock it with regularity.

“There...