In general, feeding cooked bones is not advised. If you chose to feed cooked bones anyways, you should keep the following aspects in mind:
This is the main reason why pets shouldn't eat cooked bones.
A raw bone is a solid mixture of minerals like calcium that give it strength and stability, and softer organic material like cartilage that make it ever so slightly flexible. Cooking destroys the organic material and leaves the minerals behind without the flexible scaffolding it was embedded in. That makes the bones prone to splintering, which can cause serious internal injuries.
By the way, all bones of all animals become prone to splintering when cooked, not just bones of birds.
If the bones are so brittle you can crumble them in your fingers, the risk of injuries is very low.
Pets shouldn't eat any additional salt because it can cause dehydration and urinary tract diseases. Some seasonings and vegetables like onion or garlic are even toxic to cats.
If you cooked your broth exclusively from bones and didn't add any salt or other seasoning, it should be fine. If you added vegetables or any other ingredients, please make sure they are safe for your pets, even if you think something as common as onions cannot harm them.
The chemical composition of the bones (a lot of minerals with little organic material) makes them hard to digest. You can often see dog's feces become chalky grey when they ate bones. The minerals aren't absorbed into the body and must pass the digestive tract, almost as if the dog ate a handful of sand instead of bone. This often leads to constipation, followed by diarrhea (to clean the obstruction out) and discomfort. In the worst case the colon can become completely obstructed and a vet must intervene.
If you feed your pets bones, feed only as much as they would naturally eat. Feral cats eat several rodents or small birds a day, but the bones of those prey animals are tiny compared to a chicken. Wild dogs may catch a rabbit or similar sized animal, but they wouldn't eat all the bones.
Without having any objective numbers, I would feed my dog or cat no more than a few chicken ribs a day and no more than two consecutive days. Feeding an entire carcass (like after Thanksgiving or Christmas dinners) is definitely too much.