How can I duct through a new cabinet from a floor vent opening at the wall?
Why do you need a duct? Most bathroom vanities, for example, are wide open from a slot in the floor to the louver on the kick panel. Just close off the compartment by any convenient means and call it a day. Staple some cardboard in if that works.

And parts from a big box store should work just fine. A common 2x10 or whatever size duct could be laid right in place with an opening cut in the bottom for the floor vent and the flaps flipped outward to close the rest of the opening. I think you're thinking too hard. It's just air. :)