I"m so very sorry!!! Based on NatJ's explanation, tho, it sounds like you have no other choice, for the good of everyone. Given that it can spread via human clothing, etc., I would look into whether the disease can stay in the soil, coop, bedding, etc. before getting another flock. You want to be sure your living quarters are safe for newcomers!!
I HATE having to put down any of my chickens, but over the years, we've done it several times, when there was nothing we do to ease them of their own on-going suffering. As with losing any pet or human loved one, having a recognition of mourning helps me. We live on several acres. We put the body into a little basket, carry it down to a particularly beautiful spot on the property, pick flowers or whatever is growing at the time along the way; then make a nest out of what we've picked in an appropriate spot (at our last place, it was in the folds of a giant prickly pear patch underneath a live oak tree; at our current place, it's in the crook of a willow overhanging a beautiful pond), lay the bird in the nest, place some flowers/other on and around her, thank her for being part of our experience, shed a few tears, and then leave her to return to Mother Earth (presumably with the help of a coyote or raccoon). This may not be quite your thing, but finding some way to recognize the loss that works for you may be comforting to you, just as memorials and funerals are when our beloved humans cross over.
My heart and tears are with you!!!! <3 <3 <3