The antonyms for the phrase "flagging down" could include "ignoring," "avoiding," "overlooking," "neglecting," and "disregarding." These antonyms suggest a lack of interest or attention towards the person or object being "flagged down," indicating a sense of disinterest or indifference. Additionally, antonyms for the phrase could include "embracing," "welcoming," "celebrating," "acknowledging," or "greeting." These antonyms imply a positive, enthusiastic response to the person or object being stopped or hailed, suggesting a sense of excitement or eagerness. Overall, the antonyms for "flagging down" showcase a range of potential responses and behaviors towards the act of stopping or getting someone's attention.