Oh good. I was going to weigh in that for me they are the cheapest thing around apart from woodchips that are free, but are not dry!
Kiln-dried wood shavings also will keep things drier than fresh shavings, if you can’t get pellets.
If the mold is around the roof/soffits then it’s an issue with the cold air on the outside meeting the warm air from the inside creating condensation.
The way to mediate this is to make sure the surface inside doesn’t react to the cold outside air. I would put in an exhaust fan and insulate the roof, this will make sure no condensation occurs.
I am not familiar with Killz, here we remediate mold (like that black mold) with either a 10% bleach mixture or a mold spray one can get at any hardware store. Mold needs to be scrubbed off as the roots of the mold spore grows into rough surfaces.
With houses we remediate by using a blasting medium (sand blasting but using something like sodium or even liquid nitrogen instead of sand), this removes the mold and a thin portion of the surface material to get at the mold roots. Then scrubbed with the bleach or mold spray, I detest mold, so hard to get rid of.
Now for a small chicken coop that’s a bit over kill, some good elbow grease and scrubbing will do the job. A good Spring cleaning job to do, I don’t see it too bad just some black speckles, which I cannot really say is mold or what - err on the side of caution.

