find out which section of duct or plenum it's coming from and screw a strap of heavy sheet metal to it.

How big is the furnace and how big is the duct work? The fact that the duct work is flexing every time the furnace turns on and off says to me the duct work is too small for the air flow.

In my opinion the proper fix would be to either decrease the air flow in the furnace (this may not be possible), or increase the size of the duct work. The contractor needs to examine both of these and adjust as needed. Ask the contractor to measure the static pressure. The measurement should be in the 0.5 - 0.7 range. Any higher any you will be putting a lot of strain on the blower motor which leads to premature failure. A low air flow can also cause the furnace to over heat and cause a premature failure of the heat exchanger.

Start pushing the HVAC contractor now before your 1 year warranty is up!