Lay out the metal duct's penetration point on the chimney. The metal duct needs to pitch up at least 1/4-inch per foot from the furnace to the chimney. So if your chimney is 8 feet away from the furnace, the metal duct needs to enter the chimney 2 inches higher than its height when leaving the furnace.
Drill a 4-inch hole into the chimney with your core drill. Remove the core, and clean the concrete debris from the chimney once complete.
Crimp the end of the metal duct that will enter the chimney with your pipe crimper. Insert it into the chimney and push in until tight.
Finish installing the metal duct back to the furnace. Measure and cut each piece to the correct length. Secure each joint with sheet metal screws.
Support the metal duct if the total length exceeds 5 feet. Wrap a 1-inch wide galvanized hanger strap around the metal duct and secure to the joists above with screws. The installed hanger strap will resemble the letter "U" -- with the duct resting in the middle -- if completed correctly.
Slice the tip off the end of your high temperature silicone caulk tube. Load the tube into your caulk gun, and pump it several times until you feel pressure on the trigger. Caulk around the metal duct where it enters the chimney, and tool in the caulk with your finger. This will properly seal the metal duct to the chimney.