Flag football has long been very popular in the armed forces of the United States, with the Air Force even completing a 10-year descriptive study of flag football injuries from 1993-2002. They found that the leading cause of injury was due to contact with another player, which caused 42% of their reported injuries. The second leading group of issues included slips, trips, and falls, resulting simply from the act of running during the game..
Here is a link to the actual study:
http://www.childrens.com/assets/documents/specialties/sportsmedicine/flag-football-safety.pdf