The 'wrap' is the 'case' in which the flag is stored. It's not uncommon to march with the colors 'cased' or 'shucked', which was probably more to not wear out the color sergeant rather than visibility. In this painting, the individual is uncasing the flag, and he'd the Regimental Sergeant Major, not the proper flag bearer.

The 19th Indiana was part of I Corps, and one of the first infantry regiments to arrive at Gettysburg, which was held all morning by Buford's cavalry. They were involved in heavy fighting to keep the town, and the heights behind it, until the bulk of the Army of the Potomac could arrive. The 19th was on the far left, and was soon flanked by Pettigrew's brigade, and the fighting became intense. The regiment soon attempted to fall back to a second position 100 yards to the rear.

Color Corporal Burlington Cunningham, who had already been wounded earlier, was shot in the leg, going down with the flag. A cry went up that the colors were down, and Lieutenant William Macy ordered a man to retrieve it, but the private refused. Color Corporal David Phipps, who was already carrying the regimental flag, took it, and himself was shot. Macy and another lieutenant, Crocket East, and Color Corporal Burr Clifford rolled Phipps off the flags. Macy and East attempted to case the flag, but East was shot and the colors fell again. They were picked up by Joel Curtis, who was immediately shot. Macy, attending to the wounded East, ordered Pvt. Moore to grab the flag, and Moore was shot in the hand. Moore tried to pass the colors to one of the men, who wanted nothing to do with the colors that were attracting so much fire. The regimental commander, Lieutenant Colonel Dudley then took the flag, and was shot in the thigh. Sergeant Major Blanchard ran to him and took the flag. LT Macy ordered Clifford to case the flag. Clifford moved to the rear, winding the flag around the staff. As he stopped to case the flag, a hail of musket fire enveloped him, striking the flag staff, his hat, his coat, and his trousers. Macy and Clifford managed to case the two flags. SGM Blanchard moved to take the flag, but LT Macy ordered him to stop, having seen enough men go down for it already. Blanchard appealed to the wounded Dudley, who relented.

Blanchard, who is depicted in the painting, unfurled the flag, tied the shuck around his waist, and waved it, yelling "Rally, boys!". Blanchard went down, mortally wounded. Clifford then took the flag and fell back with the rest of the remains of the regiment.

Don Troiani's Gettysburg By Don Troiani, Tom Huntington Gettysburg: The First Day By Harry Willcox Pfanz