I've never known zinna's to NOT have powdery mildew, even when grown in full hot sun. I think watering from below, as in flooding the ground underneath the plants might help. There are products, in the USA but not here in Tunisia, that are supposed to work for mildew but I've never tried them. It's my recollection that the mildew often as not comes on as the plant is quite mature, no idea why.