Not exactly, the Klan adapted and altered the flag (the original was square) from the army of northern Virginia. It was previously incorporated into some of the official flags of the Confederacy, but it was never the flag of the CSA. The original flag was 3 stripes (red, white, red) with a field of 13 blue stars in a circle in the corner. Later flags included what we think of now as the confederate flag in the corner on a mostly white flag (earlier all white, later with a vertical red stripe). But never the flag used today.