Answer: The little flying bugs are probably fungus gnats and you imported them when you brought your peony home. These little pests feed and breed in organic matter. They especially like moist potting soil. You can simply cover over the moist soil with a layer of sand or gravel or even put a temporary barrier of dry newspapers or cardboard over the soil around the peony to keep the gnats from feeding and breeding near the plant. Once they can no longer access the moist potting soil they will die off and you can remove the barrier.
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