1
general::
Phrase(s): flag someone or something down
to signal or wave, indicating that someone should stop. • Please go out and flag a taxi down. I’ll be right out. • She went to flag down a taxi.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Signal to stop, as in The police were flagging down all cars. This expression uses the verb flag in the sense of "catch the attention of, as by waving a flag," a usage dating from the mid-1800s; down was added in the first half of the 1900s.
American Heritage Idioms