Use liquid detergent in water to wash the outside of the duct (insulation). If it is less than 10 square feet that is all you need to do. You can add a little clorox if no one in your house is sensitive to the smell.
The real problem is that mold is a moisture problem. Why is there moisture on the outside of the duct? Is there air leakage around where the duct goes through the ceiling? Do you have a roof leak dripping down on the duct in the attic? Is your blower speed set too low? Do you have a dirty air filter restricting air flow. Do you have a restrictive h(high efficiency) air filter? Are you running exhaust fans constantly, which pulls humid outside air into the house to replace the air you exhaust out? Are you running your indoor blower on continuous - that will increase your indoor relative humidity 10 to
15%. Do you have an oversized AC? Do you have a plumbing leak? Do you have a damp crawlspace or basement?
Finding out where the moisture is coming from requires answers to these questions and more and requires a compentent tech. You have to look for one of those, most techs have no clue when it comes to humidity! If you clean up the mold and don't fix the moisture problem, the mold will just come back!
Good luck
Stretch