Flags appear during the middle installment of the Matrix Trilogy - The Matrix Reloaded 2003. During the fight scene with the Merovingian battle flags can be seen hanging upon the walls of the staircase.
One set of flags consists of a golden fluer de lis on green. One is a checkered flag of green and white while the other is a green cross in a similar fashion to a Scandinavian cross.
The other set of flags has diagonal stripes and large cross upon it.
Notice the infinity signs all over the shield of arms.