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You beat me to it! I was going to suggest super-glue too! Vetbond and Nexaband (now discontinued) are "purified" (for sterility) thinned down, runnier versions of cyanoacrylate glue (Super Glue) All cyanoacrylates that I know of will harden almost immediately, forming biochemically inert polymers. I haven't used it on chickens, but I've used it, and seen it used (both the surgical and regular versions) on lots of different animals, with no problems.
Walmart carries "New-skin" liquid bandage which is essentially the same as Vetbond, if you don't want to use the regular Super Glue.
If you use it, I'd recommend applying it at the skin margins, leaving a smallish gap at the bottom for drainage. After thoroughly flushing it, pref. with Betadine/water, (plain water will do if that's all you've got) apply it with a Q-tip, popsicle stick, or something similar, working quickly, and then push the flap into position. You can do the Neosporin if you'd like.(no lidocaine) I don't like using Neosporin type stuff unless its infected because of the antibiotic overuse issues. Don't use hydrogen peroxide on a wound like that, its fairly rough on the tissues, you can use it after you've closed it up, to rinse the blood off her feathers and such. (Under no circumstances get it in her eyes, it DESTROYS corneal tissue!) Check it daily to make sure its healing properly. The super glue will naturally work itself out-just like a scab.
These things always look scarier than they actually are, most animals have skin connected more "loosely" than we do, so a flap of skin peeled back, or an abcess isn't usually as serious (unless muscles are involved) as it would be on a person.
My disclaimer: I am not a veterinarian, I was an uncert. vet tech (apprenticeship OK at the time in S.C.) for many years, some nursing school, and raised various types of parrots before that. I stated what I would do/ have done with my chickens and other animals, but I do not hold a license!
Hope your girl gets better!