We've had chickens free-ranging through the bunny barn for the last forty years. We use a deep litter system, easy since we feed hay to the rabbits every day. Fallen hay makes a wonderful deep litter. The chickens happily scratch through the litter to search for bugs or fallen grain. The simple solution to the coccidiosis issue is to put a covering over each of the rabbit cages. Could be a piece of thin plywood, or as simple as a flattened feedsack (or two). Some rabbits like to chew on the feedsacks, they get a piece of thin plywood as their roof, haven't had them chew that yet, as it stays above the wire (the feed sacks can droop down within reach). If you have trouble with the 'roof' sliding off, a simple bungee cord will hold it in place.
The chickens seem to prefer a real perch to the bunny cages as a perch, so providing a wooden board (2"x4" on edge, or an old broom handle, tree branch, whatever you have on hand that they can wrap their toes around a bit to perch), maybe about 4' high and away from the cages, far enough away from the wall so they have room to perch is a good deal. Put out some nestboxes for the chickens to use to lay their eggs, with a little hay/straw inside to make a nest to cushion the eggs. Ours prefer old rabbit nestboxes set out on top of one of the cages, easy to reach, and the roof keeps any debris away from the rabbits. They don't seem to urinate/defecate near the nestbox, so that hasn't been an issue.
No urine odors, fresh eggs, less flies. It works well when you have rabbits in suspended cages. I wouldn't recommend it for those with rabbit colonies with all the bunnies on the ground, as the coccidiosis issue could become a serious problem with the poultry fouling the water.