America's Cup foiling boats sail faster than the real wind in any direction (even 3 times as much) so they always experience an apparent wind against them, same as a car or to a lesser degree a bicycle. However they don't have flags, I just checked on videos. They would blow backwards at a small angle, just as on cars.
Against the wind maybe, but I don't see how that's possible sailing before the wind. They're probably never going completely before the wind but instead alternating between broad reaches[0].
[0] I had to look that one up. Sailing terms are one of those things I only know in Dutch, and the English terms are completely alien to me in a way almost nothing else is.
Even more astonishingly are the remote controlled sail planes than not only exceed the speed of the wind, their performance is limited by the sound barrier. "Dynamic soaring" https://newatlas.com/aircraft/dynamic-soaring-speed-record-s...
From what I understand, faster-than-the-wind downwind sailing involves tacking between broad reaches, where the wind still comes in at an angle.