I don't know if you've checked with them, but Southwest Animal Health (I think that's what they're called) on First Ave. has a lot of animal medical supplies. Dunno if they'd have the vaccine, but worth looking into.
Gallo, indeed, I'm in Tucson! Been a southsider for all but two of my 33 years here in town, so people having backyard chickens is just another part of life that I'm used to. (I lived near Pima/Rosemont for two years, and while we loved being close to everything, we ended up moving back to the southside when we bought a house.) The next door neighbors keep chickens and ducks. I've asked the neighbor on the other side if she's good with us having chickens, and she was more than good with it. We're actually in the county, a few hundred feet outside the city limits out south of the power plant. I grew up a couple of blocks south of El Guero Canelo on 12th.
Nice little reminder about predators this morning. Got up to take one of the pooches out, and there was a ruckus when I opened the door. Seems the Cooper's hawk that showed up once a few months ago decided to return and perch on the roof above the door. Beautiful bird, but also capable of doing some bad things to our chickens. I'm glad we decided to not take the chicks outside for playtime today.