You will note that in the first caption the author mentions that ".....they are not like the originals used in Allach, a subcamp of Dachau" now this suggests to me that only this one subcamp ever used such metal winkels so your badge must have come from the same Dachau subcamp to be an original...is Allach part of the story you were given?
Allach concentration camp:
It was the first of seven sub-camps to supply the BMW armament factory with slave laborers, where airplane engines were produced and repaired. Starting from 1941 German civilians and about 50 prisoners of the Allach subcamp of the Dachau concentration camp were employed with production of art and porcelain. the Allach subcamp of Dachau remained the main location for fine porcelain manufacture even after the original factory in the town of Allach was modernized and reopened.