There are several synonyms for the phrase "flog a dead horse." One such synonym is "beating a dead horse," which means to continue trying to achieve something that is no longer possible or beneficial. Another synonym is "harping on," which refers to constantly talking or complaining about a particular subject or issue. "Going over old ground" is another synonym, which means to keep discussing or analyzing something that has already been resolved or is no longer relevant. Finally, "pushing water uphill" is a synonym that describes a futile effort to accomplish something that is impossible or impractical.