Final answer:
Native Americans waved the American flag at the Sand Creek Massacre to indicate their peaceful intentions and friendship with whites, which tragically were ignored, resulting in a brutal attack by Colonel Chivington's militia.
Step-by-step explanation:
The Native Americans waved the American flag during the Sand Creek Massacre as a desperate attempt to show the attacking militia that they were peaceful and friends of the white settlers.
Despite already negotiating a peaceful settlement and signaling their non-hostile intentions by flying both the American flag and the white flag of surrender, Colonel John Chivington's militia still attacked the camp, leading to the brutal killing of over one hundred Cheyenne and Arapaho people, mostly women and children.