Sword's sources from page 246, footnote 6, are Robert Bank's book, which says nothing about the 72nd Illinois, and a Confederate Veteran article written by a former member of the 41st Mississippi, which also says nothing about the 72nd Illinois.
Sword is offering conjecture in this case. There is nothing to support the 72nd Illinois' flag being captured so late. Rather, the available evidence points to the Illinois boys losing their flag before Johnson's men attacked.
Eric