Not in my experience. The best thing to do is add dry litter and use the fly traps. Honestly, we don’t usually have flies that bad. After it rains is when they’re the worst, but a fresh straw bale helps that quite a bit and they just never get horrible. Maybe it’s because we are so dry.
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I would use the area between garden and play area. No matter where you put it, you’re going to have to maintain their space. It’s quite easy really; add straw and leaves and non poisonous yard clippings to their run, which will help cover the poop and allow the chickens...