Zinnias are very susceptible to fungus diseases like leaf spot and mildew, especially in humid conditions. They love sunshine and heat and are sluggish and problematic in other conditions. The rain can be splashing fungus spores onto the leaves from pot soil.
I've had good luck defeating mildew and spotting by using commonly available fungicides such as Ortho Rose Pride or Ortho MAX Garden Disease Control. Read the labels as I think any fungicide that lists Zinnias will work - though susceptible to fungus outbreaks, for me they have proven relatively easy to save; they respond quickly once the fungus is killed. Then maintain a spray schedule regularly, as per label directions, to prevent further issues.
If you just have minimal plants to treat, get a small quart-sized sprayer at a garden center, or even a pint-sized one, and adjust the fungicide amount to only the water you will be needing in the sprayer - this may take quite some calculating unless you can use more spray on other outdoor plants.
