If the term is being used strictly, it means that one of Annie's parents, either her mother or her father, was a sibling to either William Chalcraft or Mary X.
So you may have to look further than the obvious - if Annie's parents are Mr Mitchell and Mrs nee X, and it is her mother who is the sister of Mary Chalcraft nee X, you wont find the link ubtil you have established "X" !
Just to make it harder, "niece" may be being used in a wider sense, possibly for Great-niece, and then would have to go back a further generation to find the link! Hopefully not.