If the system is sealed air-tight and a really good filtering system is in place then you should NEVER have to clean your ductwork. Most dust people see in their homes (on beds furniture etc....) is broken down insulation that is being blown into the home from the attic (venturi effect) where the duct bucket (box etc...) is not sealed at the sheetrock ceiling. On the return side, ANY leaks in the ductwork will pull hot attic air and dust into the system, clogging up everything.
You should be aware that although a substance may look like mold, a positive determination of whether it is mold or not can be made only by an expert and may require laboratory analysis for final confirmation. For about $50, some microbiology laboratories can tell you whether a sample sent to them on a clear strip of sticky household tape is mold or simply a substance that resembles it.