In the early part of The 20th Century, The United States did not refer to it's Territorial possessions as "Territories" - preferring the term "Departments". Hawaii was very to The US Military important in establishing a "foothold" in The South Pacific Region. Beginning to establish Military assets there in the early 1920s, Hawaii was administered by The US Army.
The Army Department of Hawaii Flag was designed on 1922. In addition to the "unofficial" use of The US National Colors, it was this Flag which was flying on December 7, 1941, when Imperial Japan attacked Pearl Harbor (from official Government buildings). The Flag was a Bicolor, consisting of 2 broad Stripes. The top bar was Dark Blue and the bottom was White. Centered in the Field was a Red circle with a stylized letter "H", in Yellow (superimposed). The "H" stood for the Islands of Hawaii. The Red and Yellow colors were representative of the old colors of Hawaiian Monarchy.
The Flag was used up to 1944, when just The US National Flag was flown by itself.