In hunting, the act of flushing was to scare birds into appearing so that one could shoot them. The process was also used as a military tactic for allowing enemy's to reveal their positions.
Once Jonathan Archer was able to determine the general whereabouts of the stowaway Gorn Slar aboard the USS Defiant, he had Malcolm Reed seal off one of the bulkheads, leaving the Gorn with only one escape route. The crew then proceeded to flush him out, by driving into the junction where Archer would be waiting for him. (ENT: "In a Mirror, Darkly, Part II")
As part of the Ekosians 2268 Final Decision, the Fuhrer had ordered the capital to be made Zeon-free, which according to propaganda films, had started at dawn, when the Nazi Party's "heroic troops began flushing out the Zeon monsters who've been poisoning our planet." (TOS: "Patterns of Force")
In 2372, Miles O'Brien likened watching two Klingon Bird-of-Preys emerge from a cloaked minefield in the Bajor sector that was being set off to "flushing quail." Kira Nerys then added, "Let's see how many other birds we can flush out of here." (DS9: "Sons of Mogh")
When it was determined that someone aboard USS Voyager was in cahoots with the Kazon, Tom Paris was used in an elaborate ruse so to "flush out the spy." (VOY: "Investigations")
When Voyager later had a stowaway named Reskat aboard, a magneton sweep was used to flush him out. (VOY: "Unforgettable")
In the Voyager Encounter, it was suggested by "Captain Kathryn Janeway", during her search for Tedran, that they used biogenic weapons to flush him out. (VOY: "Living Witness")