dog bites can introduce all sorts of nasties into wounds. I would give antibiotics asap.
Plus some baby aspirin for the pain.

is that white gunk some cream you put on?

some wounds heal better wet and some are better scabbing over and kept dry. You say you cleaned it first?

I would be inclined to clean it again with iodine or an antiseptic solution and trim any feathers so it heals clean of feathery bits sticking into it. And leave it open to dry. Keep her separated. If/when you put her back, then blukote it so the chickens are deterred from pecking it.

Antibiotics though, asap.

Keep her warm and quiet and calm. Feed a multivit and whatever food she will take. She will be in shock at first.

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