Some people feed their flock a treat called black soldier fly larva. You can buy the larva (google online) but some people make their own. They put dead meat up on a platform the chickens can't get to but in the run. The fly lays eggs that hatch in a few days. The larva feeds on the decaying meat and drop down off of that platform where the chickens feast on them. The chickens cannot get to the rotting meat. That rotting meat really stinks, I would not try that in suburbia.
Many of us feed dead animals to the chickens. I just use fresh killed, not old ones. Mainly rats but some possum or raccoon. Mine love a freshly killed mouse. I'll cut them open so they can get to the insides and let them feast. What they don't finish that day I take away because I don't want that stuff attracting predators to the run. Some people do that with fresh roadkill. Many people that hunt or fish feed the cleanings to their flock. I avoid old rotten meat but they are not likely to get parasites. Things that live in mammals, fish, or shellfish usually don't live in fowl.
Personally I'd let them out. I don't know where you live so I don't know how cold it's been. Is it warm enough for insects like fly larva to have devoured it. But plenty of woodland critters like mice, rats, possum, raccoon, squirrels and who knows what else have been feeding off of that carcass and it doesn't hurt them. Some birds like crows and jays have probably been feeding off of it. If you watch certain nature channels you soon see that a carcass in the wild doesn't go to waste. Things eat it, even after the meat has gone bad. Before they were domesticated chickens were some of the critters that would have feasted on a carcass like that.
