A flophouse was a place that offered very cheap lodging, generally by providing only minimal services.
The term "flop" was part of vernacular of the 1930s United States of America on Earth. Captain Kirk was momentarily perplexed by Edith Keeler's use of the term "flop" during his visit to that era. (TOS: "The City on the Edge of Forever")
While visiting Sigma Iotia II in 2268, Kirk ordered Scotty to transport the men on the other end of a telephone call to his current location by using language more appropriate to the 1920s style era that the planet had adopted as their own, specifically telling Scotty to "locate the man on the other end of the blower and give him a ride to this flop." (TOS: "A Piece of the Action")