I would tend to think the 1st Rhode Island Battery A with 6-13 Pounder rifled guns must have lost a flag. The battery was captured along with the big 30-Pounder Parrot rifled gun that some idiot dragged across the river. The big gun was captured. The Union flank "attack" was slow to form because they brought that huge 30 Pounder with them.
Burnside's Brigade was the first to cross over and they tangled with Wheat's Battalion. The 2nd Rhode Island Regiment was the first regiment to take the field. Evans and Wheat were heavily outnumbered, at least 800 CSA soldiers to 3,500 Union soldiers. When Bee first arrived he wanted Evans to fall back to Henry House Hill. Bee did not like the idea of sending the men up to Mathew's Hill.
Today some of Mathew's Hill is clear but there are woods to the right and some Civil War signs. Bee brought up Bartow's 7th and 8th Georgia and the 4th Alabama. All of these regiments would lose over 200 men.
Either Wheat's Battalion captured a flag early in the fight or when the Union soldiers retreated. To lose 200 men was nothing, all the regiments were very large.
From Terry L. Jones book "Lee's Tigers" page 51 said "They were outnumbered six to one, for several minutes the 2nd Rhode Island and Wheat's men went at it." Wheat's men were hiding in the bushes and behind trees. Not fighting the stand up, we shoot, you shoot type deal.
When Major Wheat was hit the bullet went through both of his lungs, he was carried on a blanket with a the flag "Old Dominion Guards over his body".
Wheat lost 8 men Killed, 38 wounded and 2 missing.