I think that some trolling has been going on, but in case the question was
for real, the answer is: Repair the duct, screw the pieces together. The
duct- in fact any duct- should be mechanically sound before any sealing.
Duct tape, as used in the trades, is used on some ducts to overlay a seam,
but the seam itself must be tight, entirely closed and sound before applying
the duct tape. I've seen inspectors use a pick or knife point to test just
that issue.

For a vent pipe, this is even more important. Personally, I've never seen a
professionally installed water heater, boiler or furnace vent pipe held
together, spliced or even reinforced with duct tape. It'll burn, dry out or
fail. Possibly the aluminum "tape" could be used, but even that has an
adhesive that would probably fail due to the heat.

You're much better off replacing the bad section of the vent, from the draft
hood up. The cost isn't that much and you're going to be a lot safer.

Nonny