Slice the old fire-rated sealant covering the space between the flue and the brick with a utility knife to cut through the sealant. Pull the old sealant from the space.
Pry the old backing material from the space surrounding the flue, using a slotted screwdriver to dig the old fire-rated rope or mineral wool from the gap. Flue installers use fire-rated rope and mineral wool as backing material.
Inspect the space between the brick and the flue pipe. If a brick touches the flue pipe, hold a chisel's blade on the part of the brick that touches the flue. Strike the chisel's handle with a hammer until the part of the brick that touches the flue pipe breaks off.
Clean the brick and flue's surface with a wire brush. Use the brush's bristles to remove any remaining sealant, paying special attention the the brick's mortar joints.
Pack the space surrounding the flue pipe with either a fire-rated rope or mineral wool. If using fire-rated rope, run the rope around the flue pipe two full revolutions and cut the rope to size with the utility knife. Push the fire-rated rope down into the gap until the top of the rope rests about a half inch below the brick's surface. If using mineral wool, grab a handful of the mineral wool and force the wool into the space surrounding the flue pipe. Push the wool into the space until the top of the wool rests about a half inch below the top of the brick. Repeat this procedure until you have filled the entire space surrounding the flue pipe with mineral wool.
Run a bead of fire-rated silicone across the top of the fire-rated rope or mineral wool that surrounds the flue pipe, using a caulking gun to apply the silicone. Continue to add additional beads of the fire-rated silicone to the space surrounding the flue pipe until the top of the silicone extends about a quarter inch above the brick's surface.
Press the fire-rated silicone into the space between the brick and flue, using a spoon's curved end to give the silicone a smooth surface. Let the silicone cure for 24 hours before using the flue.