I dont see the 2nd Delaware in the Union order of battle at 1st Manassas. I think you mean the 2nd New Hampshire which was in Burnside's brigade and saw heavy action first. They fought against Wheat's Battalion, the 4th South Carolina and elements of Bee's brigade.
From this information, I assume now that the 2nd New Hampshire must have lost a flag early in the action. Probably Wheat's men were taking cover in bushes and behind trees and with accurate fire picked off targets. With all that smoke they started firing at the flag when they could not see a target. The 2nd New Hampshire's commander, Col Gilman Marsten was wounded.
None of the Union brigade that was on the battlefield were anything near their "paper strength". Many had fallen out of the hot dusty march from Washington City. Many union brigade were 50% their "paper strength". Wheat's men opened the first shots at close range when Burnside brought his brigade in first.
I read a report that when Major Wheat was wounded the battalion broke apart and the men fought in groups and did a knife attack on the 11th New York and captured 2 cannons from Sherman's brigade.
I will go to the LOC next Saturday and see what I can find on Union flags captured at 1st Manassas.