In 2285, Kruge noted that with the Genesis Device, his officers could be sitting happily on their homeworld, with the exception of the flag of the Federation soaring above instead of that of the Klingon Empire. (Star Trek III: The Search for Spock)
It was also displayed in Deep Space 9's briefing room during various official ceremonies, such as Worf's court martial, and the induction ceremony when Bajor (almost) joined the Federation. (DS9: "Rules of Engagement", "Rapture")
In accordance with an old Earth tradition, the flag was flown at a baseball game on the holosuite on Deep Space 9 when the Niners and the Logicians played a game in 2375. They also played the Anthem of the United Federation of Planets, taking their hats off and facing the flag. (DS9: "Take Me Out to the Holosuite")
The first "Flag of the Federation" in Star Trek was visible across Spock's coffin in Star Trek II: The Wrath of Khan. As it hadn't been designed yet, the flag was missing from the Enterprise's conference room throughout The Original Series.
According to the Star Trek Sticker Book (Pg. 9), by Michael Okuda, "At one time, it was thought that the three bright stars in the starfield might represent Earth, Vulcan, and the Klingon Homeworld, since during early episodes of Star Trek: The Next Generation it was thought that the Klingons might have actually joined the Federation. When later episodes made it clear they had not, the three bright stars were left undefined."
As described in Star Trek: Action!, in Deep Space Nine "Tears of the Prophets", someone was looking at the photon torpedo prop and couldn't quite put their finger on what was missing. They then disappeared, and came back with the Flag of the Federation to drape over it.