Flag of the United States Assistant Secretary of the Navy for Aeronautics.  The position existed from 1926 to 1932; I'm not sure if this flag was in use during all or just part of those years.  The position was resumed in 1941 and renamed as the Assistant Secretary of the Navy (AIR); by that time however the position of Undersecretary of the Navy had been created in 1940, and there were multiple Assistant Secretaries of the Navy.  At least by 1943, the Undersecretary had their own flag, while the Assistant Secretaries (including the AIR assistant) all used the Assistant Secretary flag, so this no longer in use by then.

The flag design is the same as that for the Secretary of the Navy except that the field is white and the anchor and stars are red (the Assistant Secretary's flag is similar except the anchor and stars are blue).
Modified from File:US-SecretaryOfTheNavy-Flag.svg
Carl Lindberg