It looks like flask # 365 in Ray Riling's book, "THE POWDER FLASK BOOK". (p. 291). The author classifies it as a "Shell & Bush" design.
The flask was made by American Flask & Cap Company. (p. 286) The American Flask & Cap Company was located at 52 Beekman Street, New York, with its manufacturing plant at Waterbury, Conn. It was formed in 1857 and was taken over by Waterbury Brass Company in the late 1860's.