I have good luck simply direct-sowing zinnias in spring, after our average last frost date.
By "mildew" do you mean damping off, where the stems pinch in at about the soil line & the seedlings keel over? Or do you mean powdery mildew, which honestly I've never seen on my seedlings, although I do see it sometimes out in the garden... ?
Either downy mildew or botrytis (grey mold) where your have fuzzy, raised moldy stuff (fruiting bodies) on plants that are past the damping off stage. I worked at a nursery where we had limited success starting these three from seed. When you're trying to have blooming plants ready to sell by Memorial Day you have to start early, usually mid-February, when sunshine and heat are hard to come by in CT. Most commercial growers go straight to the chemical fungicides. I'm not about to use that stuff inside my house, but I'd still like to be able to get a jump on the season. I've never been successful with any of these.
I've had downy mildew on houseplants in the winter... better air circulation and warmer temps both seemed to help, so maybe heat mats would be of use. There are less harsh remedies... sprays with milk, or with hydrogen peroxide... google, and you'll probably find recipes, or post over in the Garden Pests & Diseases forum: http://davesgarden.com/community/forums/f/pad/all/