The flag in question that appears on the seal of Winchester, Virginia is the battle flag of the Army of Northern Virginia. This post war flag is also known as Beauregard's flag, the rebel flag, Dixie flag, Southern cross, and the "Virginia battle flag".
When the Confederate States of America formed in February 1861, the inclusive states seceded because they feared that the election of Abraham Lincoln, a Republican President, would lead to restrictions on their right to do whatever they chose about the question of slavery. In fact, the Constitution created by the Confederate states differed little from the U.S. Constitution. Adopted March 1861, differences included a six year term for president and VP and upholding the institution of slavery.
The main Confederate Army, the Army of Northern Virginia, surrendered April 9, 1865. They carried the Confederate battle flag. However, the Confederate national flag was different from the battle flag. It had a red bar on the right end of the flag, was primarily white, with the "battle flag" in the upper left hand corner. The creator of this flag, William T. Thompson, shares his interpretation of the true meaning of Confederate flag:
As a people we are fighting to maintain the heavenly ordained supremacy of the white man over the inferior or colored race; a white flag would thus be emblematical of our cause. Such a flag would be a suitable emblem of our young confederacy, and sustained by the brave hearts and strong arms of the south, it would soon take rank among the proudest ensigns of the civilized world as THE WHITE MAN'S FLAG."
Thompson's flag was known as "The White Man's Flag" indicating white supremacy, or "The Blood-Stained Banner". Thompson's version of the Confederate flag was known as the "peace" flag.
The "battle flag", originally rejected by the Confederate Congress "Committee on Flag and Seal", was designed in 1861 by William Porcher Miles, Chairman of the Flag and Seal Committee. General Beauregard suggested having two flags: a "battle" flag and a "peace" or "parade" flag. The "battle" flag was recommended by Beauregard because the flag of the Union and Confederacy were confusing the commanders during battle. From afar, "Stars and Stripes" and "Stars and Bars" were making battle strategy difficult. Thus two Confederate flags were created.