Green’s Dictionary of Slang

(orig. US black) a brothel; a hotel where one can go with a whore.

1935		A.J. Pollock Und. Speaks.
1939		D. Maurer ‘Prostitutes and Criminal Argots’ in Lang. Und. (1981) 117/2: riding academy. A cheap hotel where one may take a prostitute.
1952		W.R. Burnett Little Men, Big World 34: Don’t suppose the place has changed much. I haven’t been there in fifteen years. They used to call it the Riding Academy.
1955		F. Kane ‘Return Engagement’ in Best of Manhunt (2019) [ebook] ‘I got other things on my mind. Running a riding academy like this ain’t the best way to grow old gracefully’.
2000		(con. 1940s–60s) Décharné Straight from the Fridge Dad 154: Riding academy Whorehouse.