Set up a ladder in front of the stove. Open the cabinet located directly above kitchen vent hood.
Wipe the connection between the vent hood and the duct with a rag. Wipe the remaining duct seams with the rag. Ensure all seams are free of dust. Allow any dampness on the duct to dry before continuing.
Wrap metal foil tape around a cleaned seam. Ensure the end of the tape overlaps the tape attached to the roll by three inches. Tear the tape with your hands. Remove the paper backing from the torn length of foil tape.
Align the center of the tape with a cleaned seam. Press the end of the tape to the duct. Pull a squeegee over the tape to adhere it to the seam. Close the cabinet doors.
Move to the attic -- if applicable. Repeat the process of cleaning each seam. Apply the tape as described to seal all remaining seams.