What is on my Lilac Garden Phlox?

Sure looks like some sort of powdery mildew.

Use a mixture of soap and water in a spray bottle. Spray as needed.

If powdery mildew, Neem oil, diluted according to the bottle, works well. Brown spots could be a fungus or mites. call your local extension service and see if there is a Master Gardeners program or extension agent, or even take a leaf to a good nursery where you will find a knowledgeable person who can identify the problem. Hard to do from your limited photo.

Thanks to all who replied. I’m going to start with soapy water spray. If that doesnt work then neem oil.