Final answer:
The Indian chief who always carried a flag and medals from President Lincoln for protection was Chief Iron Tail.
Step-by-step explanation:
The Indian chief who always carried a flag and medals from President Lincoln because he thought that these would protect him was Chief Iron Tail. Iron Tail was a prominent Sioux chief who fought in multiple battles, including the Battle of the Little Big Horn and the Great Sioux War of 1876. He believed that the flag and medals from President Lincoln would offer him protection from harm.