"The invention of numerous fluting devices during the period 1860 to 1890 revolutionized previous methods for crimping, ruffling and pleating fabrics. These new fluting devices produced ruffles by pressing dampened fabric between two intermeshing, heated ribbed (fluted) surfaces." David Irons, Irons By Irons, page 55.
Here is a list of some fluting machine patents in class 223/32 (Apparel Apparatus/Intermeshing Teeth).
This rare fluting iron is referred to as the Meyer's Goat. It's a combination, twist handle machine by F. Meyers, goat profile on front, hinged at front, patented Feb. 18, 1872. Length 6 5/8." As seen on p. 55 of Irons By Irons.