I have never had a problem with mildew on peonies before this summer. We have had an very unusual summer with about three times as many over 90 f. days than we usually have with high humidity. As a consequence, one of my peonies started to develop mildew. It was in its early stages. To one gallon of lukewarm water, I mixed one tablespoon of baking soda, one teaspoon of oil (you can use horticultural oil or canola oil) and one teaspoon of regular dishwashing liquid. Shake well. Place portion of mixture in a spray bottle. Then spray the plant. Do this when it is cool and when the plant is not in sun. I did it in the early evening. Repeat in 10 days to 2 weeks, or if it rains.
It worked very well and by the next day, the mildew was looking brownish and "sick". So, I decided to try this mixture on a phlox that always gets mildew. It worked! Neither plant showed any ill effects from the spray.
I am hoping for a summer with more regular temperatures next year