Green’s Dictionary of Slang

1. (US prison) a short sentence, max. one year.

1909		‘The Lang. of Crooks’ in Wash. Post 20 June 4/1: [paraphrasing J. Sullivan] A valentine [is] a short jail sentence.
1910		Spokane Press (WA) 22 Sept. 7/3: When a thief serves a short time in prison he calls it a ‘Valentine’.
1919		NY Tribune 8 June 7/5: A ‘valentine’ is a short sentence.
1924		G. Henderson Keys to Crookdom 422: Valentine. One-year term in prison.
1949		Monteleone Criminal Sl. (rev. edn).

2. (US police) a reprimand, a punishment.

1930

E.H. Lavine Third Degree (1931) 175: In some precincts, the men belonging to the local political club would insist on picking out their posts and would escape reserve or extra duty [...] If a conscientious or over-ambitious sergeant gave them a ‘valentine,’ the captain would bawl him out for looking for trouble.