"cheap hotel," hobo slang, 1904, probably related to slang flop (v.) "lie down for sleep" (1907); see flop (v.) + house (n.).
In one of [Cincinnati's] slum districts stands the Silver Moon, a "flop house" (i.e., a house where the occupants are "flopped" out of their hanging bunks by letting down the ropes) .... ["McClure's" magazine, November 1904](But this explanation is not found in other early references.)
A cheap and sordid rooming house or hotel, esp one with dormitories for men; chinch pad, fleabag: I'm spending my nights at the flophouse (1923+)