I am sorry this has happened, and I know you don't want dog or culling comments, but I feel the need to make them anyway. I have to have this 'talk' with people on a regular basis- never pleasant, but must be said.
Having a dog that attacks chickens is not unusual, many have a strong prey drive, if we choose to keep prey items and dogs/cats in the same household, we do our best to keep them apart. What bothers me is NOT that the attack happened (though it is sad), but that the dog did not stop when you intervened. My dog has attacked a chicken twice, I intervened- he knows drop it, he knows come, ect. One chicken was killed, one ended up being fine- but I never had any doubt about my ability to control him once I realized what was happening (he is a 90lb dog). If this dog has a prey instinct strong enough to rip apart and chicken, and it is not trained or not socialized- it should not be at your house, rescue or not- it is a dangerous dog. Dogs are social animals, and should not be kept alone in a pen (for 3 years) this type of set up promotes aggression and territorial behavior. If this dog cannot live as a social animal because it had a bad puppyhood and cannot be trusted- you should have it euthanized. Next time it might be a cat, a small dog, several chickens or a child.
For the injured chicken- living with no wings will be hard, but not impossible- chickens are very adaptable. She will have trouble dust bathing, getting on and off of perches, and will fall over alot as she will have trouble with balance. You will need to create low perches, and watch her more carefully for lice.
As we cannot see her, we cannot really asses her injuries- but if she has had her wings ripped traumatically off by a dog (think bacterial contaminated wounds) - she should see a vet- she deserves pain medication stronger than aspirin. She needs systemic antibiotics, she needs dead tissue removed, and healthy tissue closed over any exposed bone. This will give her the best possibility of a good outcome, and she will heal faster and with less pain. I think if you cannot do this for her, you should humanely end her life.