Can you wrap HVAC Ductwork with heat shrink film to seal leaks?
What you linked to may be the simplest solution for now since the HVAC guy goobered up the duct work with mastic. 

Otherwise the tape that J Hirsch linked to at HD would be the fix for it, and it still may if the mastic that was used will allow it to hold, if the duct is NOT flex duct, so there is backing where the tape is applied. If it is flex duct and there is backing, like where the duct attaches to the collar at the unit, then it will work...possibly. Again the mastic may keep it from bonding well. If the duct is clean, free from dust, that stuff will stick really well.

Using the heat shrink stuff may come at a great cost unless you go to a marina where they use the stuff regularly for winterization for the upper deck of the boats in the storage yard. But that may be really wide stuff, but a 3 ft wide strip could be cut off the end and it may get you a 12 X 3ft piece for example.

Explain what you need it for and you may be surprised, the folks may even give you tips on how to work with it. Whenever I use something that is not the norm for a particular item, the folks that have it, once they understand what I am needed to accomplish are usually more than willing to help. Then..... sometimes...