I have chickens on the ground in my rabbitry. The cages hang above.
There are some hazards even to that setup. I've heard there may be diseases that can pass from chickens to rabbits. Never had a problem, but I only keep a small closed flock of hens.
I don't add DE to the floor to keep the birds from kicking up too much dust.
And once, a newly-brought-in doe was unexpectedly pregnant and birthed on the wire in a bottom level cage (one of those situations where the person selling me the rabbit promised that she couldn't be pregnant :roll: ) It was cold so they probably died quickly, but by the time I found them the chickens had pecked at the babies through the wire.
It was the most horrible thing I'd ever seen pertaining to rabbit raising.
After that experience, I've always been careful to keep does in higher level cages where the birds can't reach, just in case.
My hens are sweet to people and each other and not cannibals at all...and they never peck at adult rabbits or juniors.
If they will eat newborn bunnies, I'm afraid most people's birds would. Hens in a colony would probably learn to destroy every nest of popples they could find.
The other thing would be rabbits coming in contact with chicken poo. To me, that would be gross.