Waste of time and effort

I think you need a good sheet metal guy. I would take the cap off and inspect the interior of the flue and make sure it is in good shape.

I don't like the "Flat cap" the flue extends through. I would have a new cap made with some pitch to it. The new cap would have a sleeve welded or soldered to the new cap and then counter flashing put on the flue to cover that and I would extend the flue pipe up another foot or so and then put a new cap on the flue if you think the old one is no good