mm wrote:
I was in an appliance parts store and they had several pieces of
heating duct in the corner, including a piece that I will need two of.
This place doesn't sell the stuff. It was just stored there.

It is like a very short rectangular HVAC interior duct, that clamps to
metal ducts at each end, and has 4 inches of heavy vinyl in between.

Like 15x20x4 inches.

Is there a name for what I saw?

It's meant to go between the furnace/AC and the rest of the house
metals ducts, partly so furnace vibration won't get transmitted to the
house. Although it seems not every installer uses them.

The label on it said flex duct but when I looked that up on the
web all I found were long truly flexible ducts with built-in
insulation that contractors now use sometimes to go from the main duct
to individual rooms.

Try flex duct connector or flexible duct connector or duct connector.

Jon