I went and posted a question on the Virginia Board, about units at the Battle of Elthaim's Landing. There was a news article that identified some of the units (see http://history-sites.com/mb/cw/vacwmb/index.cgi?read=3814 ) One of the units was the 6th North Carolina.
So, based on this news article and the one that started this thread, it appears that the Sixth Flag captured, belonged to the 54th North Carolina and the Sevent Flag Captured belonged to the 6th North Carolina. The key being reference to Ethain's Landing on the 6th's Flag.
54th NC Flag -
a sixth by James H. Littlefield, of company I, 5th Maine, inscribed with the names of "Cedar Run," and "Manassas" "Second Harper's Ferry," "Sharpsburg," "Winchester," Chancellorsville," "Fredericksburg," "Gettysburg;"
6th NC Flag -
the seventh by Corporal E. P. Blondil, of company D, 5th Maine, inscribed "Manassas," "Seven Pines, " "Gaines's Farm," "Malvern Hill," "Ethain's Landing."--