Can you tell us where you found this, who said it, when and why he or she said it, and to whom? Providing context is a requirement here. There's a good reason for it: "drop the flag" has many meanings, ranging from paying honor to a fallen soldier to beginning a trip in a taxicab. We can't tell which it is from the phrase alone.
One woman informs another one about the derby that she is organizing and asks her to "drop the flag on Derby Day".
Could it be the literal meaning? That she wants her to actually drop the flag to start the race?