The robes and pointy headgear of the KKK are copied directly from the costume of the penitentes in the processions of Semana Santa (Holy Week) in Seville, Spain.
The pointy headgear is a dunce cap. The point indicates that the mind should be focused upwards, toward Heaven. Carrying the religious images in the parade could be considered a great honor, and of course, that could bloat someone's ego, so they cover the entire body of the image bearer so he cannot be recognized. The Confederacy's ambassador to Spain hung out in Seville during the Civil War, unsuccessfully seeking the aid of Queen Isabel II, and after the War, returned to help Nathan Bedford Forrest found the Klan. That is how the Klan got its uniforms. The flaming cross was another bit of ancient lore.
In the 1860's, Europeans were engaged in defining all the old national traditions and folklore, so there was a lot of interest and many articles in newspapers and magazines about ancient folklore.