A Kilz type product was used over some wood with black stains which we now realize may have been mold. What should we do now? Can we treat the KIlz painted wood with a mold killer now?
I would be sure and get rid of the source of the mold as the kilz did not stop it. I am not a handy person, but, for mold I would consider a thorough job is essential to the existing mold not just painting with kilz as there are future unforseen health concerns.
If it was oil-based Kilz, you'll need to remove it. Rather than the previously suggested sanding, I'd recommend applying turpentine or mineral spirits and scrubbing with a disposable scotchbrite pad. Sanding has a greater risk of spreading mold spores, not to mention being more effort.
Bleach is ineffective at killing mold on porous surfaces such as unfinished wood. Ditto most "mold killers" you'll find down the cleaning aisle at most stores - most specify this in the instructions, some you have to check the website to find out. Products for porous surfaces exist, but can be hard to find and identify. Foster's 40-80 is the only one I know of that advertises that it kills mold on porous surfaces, but I've read that plain old white vinegar does the job, too (I discard moldy material, so don't take this as an endorsement of either - I've never considered the risk of ineffectiveness to be worth trying 40-80 or vinegar).
Do NOT use a "mold killing" primer for the same reason. They work only on the surface, while mold can survive deep in the wood, just waiting to be released. This is usually fine on previously finished bathroom paneling or wallboard provided the mold is only growing on the surface, but not on wood. Eliminate the mold, then use Kilz.