If your taking the birds out of the area, or can do, the best for flys and odour is the hydrated lime. Yes you sprinkle it on or use a drop spreader and then till it in for fast recovery or water it in but will take longer before birds are back. It will work instantly on odor and flies and in the process correct the pH so that if your reseeding the plant has a better chance. I used it in the muddy runs when I lived at the coast and it's great but you have to rotate birds out.
Dolomite or Dolopril will work too, neither do you have to take the birds out. Sprinkle, till or not and water or not. You can also use this freely in or under the bedding in your coop without any protection for the birds. I concentrate it under the perches under and in the bedding. Makes for way less smell, flies and easy to clean up as it's a drying agent.
The advantage of the hydrated lime in the short term is that if you had sick birds and tilled it in as well as made white wash for the walls and fencing you might break the cycle of cocci, mites, lice, some bacteria and viruses. In cement floor barns or coops it can be used as a wash after taking out the bedding before you put new in to make the floor sterile. For wood often it's painted on and left to dry just like a whitewash fence. Down side is it's done quick. It's a one shot wonder kinda thing.
Adding Dolomite or Dolopril will not make things sterile the day of application but it tips the pH out of favor for most bad bugs and by drying makes the living conditions much harder. It lasts as long as you can see it or it seems to be drying.
Edit to add that we found the confusion in the past is what the supplier called the product. Some call the hydrated 'Quick' lime, and some call Ag lime 'natural' or rock lime and some call it Hydrated. Hydrated refers to the ability of the chemical to react to water, and how much of that ability is already taken up. Totally hydrated lime is no longer able to react and safe to touch your skin, but most hydrated lime sold is only partially reacted so that it mixes better. Read the bag! Contact the supplier if in doubt as to how to use it.