Most furnace manufacturers specify that flexible section of the ductwork to isolate the vibrations that may originate in the furnace from being coupled to the metal ductwork. In my unprofessional opinion, it was not installed per the manufacturer's instructions, and they should resolve that at no cost to you...a pro should install per the manufacturer's instructions. Now, some things are optional or only recommended, and with that, there's some wiggle room...depends on how it is stated in the installation manual.
That being said, having it may not stop that noise from being heard upstairs. That noise could be a relay, it could be the igniter (if it is a piezoelectric rather than a glow stick igniter), or maybe even the gas valve opening. Metal to metal conducts noises better, but some will still make it upstairs. Can you isolate the noise if you are down there when it happens?