peroxide is not for deep wounds nor should you ever use peroxide on any chicken/ dog you may want to show. Peroxide is a great cleanser, however there is a bad effect of deeper scarring when using peroxide. I would use betadine to deep clean. make sure the bleeding is stopped and let the betadine dry. (best to dry the betadine without blowing on it. it needs to dry in a clean windless environment) Now decide if you need to stitch it up... if you do please use proper steryl stitching sutures (the needle in built in to my thread and is in a steryl pak. , or a surgical staple gun (either can be purchased from a place called jeffers which is online). If you are going to close it with sutures, the wound does have to make sense. I saw where a person was successful using super glue to close a wound, but I have never tried it myself. I really do not know lots about chickens yet, but i would see if there is a good cleanser that would promote feather growth. i would then apply antibiotic ointment and/or if the wound is serious enough, I would put on oral antibiotics as well.
Here in Missouri, the owners of the dogs responsible would have to pay you for any losses of your livestock who are on your property when the attack was made. check with your states laws to see what if anything can be done to stop these attacks on your property.
I am not a vet, I only write from my personal experiences with my own animals. you should always check with a licensed professional before making changes in the care of your animals.
Donna in Branson