Flag vs flagstick

[Martin B]

On the green, the flagstick was pulled and put on the ground. A golfer putted and the ball went over the flag, that was lying flat on the green, without touching the metal parts of the flagstick.

I know there's a penalty for hitting the flagstick, but does the rolling over the flag count?

[Kilroy]

Not the exact decision but it answers your question

17-3/5 Flag Struck by Ball When Flagstick Attended
Q. While the flagstick was being attended, a player’s ball struck the flag attached to the flagstick. Did the player incur a penalty under Rule 17-3a?
A. Yes. The flag is part of the flagstick.