The Appleton Boat Club is listed in Lloyd's Register of American Yachts, 1912, as organised and incorporated in 1907. Its station is given as: Foot of Eldorado Street, Appleton, Wi, on the Fox River.
The last mention of the boat club I found in the Internet newspaper archives was for 1940. According to Images of America: Appleton, by the Appleton Historical Society, the Appleton Boat Club later became the Appleton Yacht Club, but the site of the latter makes no mention of that.
The Appleton Boat Club burgee is also shown in Lloyd's Register of American Yachts, 1917, though the club apparently isn't otherwise listed there.
This time its burgee is depicted as a ca. 5:8 Red triangle with in the centre a white bold condensed sans capital 'A', half of the hoist high.