Vermont's state flag (authorized in 1919) features the state coat of arms against a field of blue. Description for Vermont's coat of arms (from Vermont's Secretary of State - Vermont State Emblems):

"The shield may be of any shape, with any sort of border or none. There must be a landscape of natural color in the foreground or base, with high mountains of blue above and extending into a yellow sky. There must be a pine tree of natural color extending from near the base to the top; sheaves of grain three in number and yellow placed diagonally on the right side; and a red cow standing on the left side of the field. The motto, badge, crest, and scroll must conform to the description. "

Source:

Vermont State Emblems: Vermont Secretary of State

Links:

State Flags - 50 states List
National Flag