If you do want to try screws to secure the duct to the ceiling and floor to stop rumble, get the self tapping countersunk head style. I would predrill a small hole in the metal first so you dont push the duct inwards.

Realize if you will I don't understand how screws are supposed to help but I can imagine more than a couple of ways they could make things worse. As a benign,can't hurt remedy,may I suggest (A) drilling a hole (from above or below) through which the straw on a can of "WINDOW AND DOOR"foam will fit. (B) squirt half a can of foam into cavity. (C) wait 3 days to see if problem is solved (D) if problem presist's,drill another hole 18"from first and repeat B&C until it's gone. If that doesn't cure it and you can't forgetaboutit,the foam is easily ripped out when floor is opened.

If screws dont shore up the duct to stop rumbling, you put a piece of foil tape over the hole after you rip it all out. Same difference. Either way would work, what you want is the duct to stop being loose enough to move.

Also, make sure the furnace is decoupled from the ductwork with a flexible coupling.