1 Sweeping a regular open fireplace can cost $79-$200. 2  Cleaning a freestanding wood burning stove with liners runs $109-$209. 3  Cleaning wood burning stove inserts with liners is about $109-$149. 4  For Do-It-Yourslefers, a brush and rod set runs about $20-$30 for a masonry chimney and $29-$36 for a metal chimney. Stove inserts that do not have liners that run to the top of the chimney need to be pulled out for access and run an extra $40-$50. 2  Any insert pipes that have to be removed to be cleaned can cost around $20.