The Animatrix was a series of short animated prequels for the Matrix Trilogy. It was a collection of nine stories that expanded and explained some of the back story. In The Second Renaissance the 'flag' of the machine-robot nation is revealed as a union of white with black.
It is first shown as an imprint on cars made by 01 - the machine nation.
Arms of the Machine Nation
Here the apparent arms of the 01-machine nation are shown. It is a shield cut in three sections vertically. On the left side it is white, in the middle is a thin grey metal division and on the right it is black. In the center is a thin grey line below the navel. At the honor point tilted to right is a grey disc. It is crowned with six metal extensions. In the compartment is a silver V shaped chevron. Notice 01 white and black badge in the lower left corner.
Here a package shows the white and black badge of 01-machine nation.
After the governments decide that the unrecognized and economically powerful nation of 01 must be destroyed, war results.
On the left a humanoid robot riding another robot horse leads the 01 armies into battle with the nations of the world. The flag of 01 is torn and tattered.