We have a black dust problem with the ducts in several rooms.
we do have air vent ductwork that is from 1997.
It sounds like your ducts are excessively leaky allowing dust to be pulled into the ducts and delivered throughout the house.
A duct test along with sealing them is definitely in order along with a maintenance and cleaning check of the unit.
You may also wish to have a full diagnostic energy audit done to help find any other issues.