I feel that the military gets underestimated a lot especially in the media, movies & books. I'd understand if it's a third world country but a developed nation with an established military force is way more capable than what writers make them out to be. Hell, they're usually written to be ineffective so that the plot will work.
In this scenario, it is not a global crisis nor is it a virulent & infectious epidemic like a zombie apocalypse. That makes it way easier. The National Guard and Police will likely be responsible for cordoning off the town. There are QRF(Quick Reaction Force) and RDF(Rapid Deployment Force) that will be the main body of the operations. They're usually on redcon 1-2 readiness(immediate) or 2-4hr notice to move(ntm). They can get onsite quick, especially when it's a homeland crisis. I'm not from the US so i reckon their army airborne battalions and tier 1 & 2 SOF teams will be the ones responsible. Response time would be swift, this is not merely a riot, it's an immediate national crisis.
Drones and planes will be circling the area of operations(AO) within hours to gather intel. You have satellites too. Now night vision won't work in the chem clouds but Thermals & Infrared Imaging will but with a shorter effective distance. This is only the tip of the spear. There are other more effective sensor tech unavailable to the common soldier but available to Intelligence Agencies & Specialist Units like Hyperspectral Imaging, Polarimetric Imaging & Millimeter Wave etc.
Due to how the chem clouds work in disrupting electronics, which is a point of contention as over hang power, landlines and their handphones aren't adversely effected, the drones may or may not work. Which can be combated using airtight shielding material or fairings and utilize fiber optic cables instead of radiowaves. Most military grade vehicles come with limited hardening & shielding. The specialized vehicles though come with better grade protection and resilience so they can likely work in the AO. You'd be surprised how much money is wasted by the military on what-if contingencies.
MOPP gear may not be as effective in this chem cloud so they'll use self-contained breathing gear. Visibility is the main issue, Thermals & IR might get disrupted. However, there are advanced versions that are emp hardened, with electronic resilience and component shielding mainly used by Specialized Units. These have a high likelihood of working within the AO. Goes the same for VHF/HF equipment and manpacks used for comms. Worse come to worse, you go low tech and lay lines(D cables) with an exchange, create Combat Outposts & Staging Areas to maintain a line with Bn HQ.
It's also a homeland crisis so the military's CBRN(Chemical, Biological, Radiological, and Nuclear) wing will be working side by side with civilian CDC counterparts and other Subject Matter Experts.
Concurrently, the military can air drop supplies to trapped civilians & scatter flyers on evac instructions. Realistically in a setting like this, a dead town with a low population, they can afford to do multiple low-litter air evacs(lesser pax) instead of asking civilians to gather up themselves.
Speaking of air evacs, heli downwash can clear the clouds. The rotor noise can be used to gather infected to mow them down. Thinning their numbers and distraction tactics can allow insertion teams safer navigation through the town. One of many strategies available to the military. The current wars we have showcases the true human ingenuity we're capable of.
As for command, militaries have evolved a lot over the years and adapted a more flexible chain of command, allowing independent decision making within reason, with focus on leadership qualities specifically to deal with incompetence & infighting. If it is third world & developing countries, hegemonies, junta regimes, i can see this being an issue. If anything, the real hinderance will be Politics. The problem will always be Politics. But in this kind of scenario, it is in the best interest of politicians to quickly resolve the situation to maintain decorum and restore public confidence.
I'm just a regular airborne infantry so my knowledge is limited. I'm just touching the surface and do not know the full-spectrum capabilities of the military, police and government agencies. Specialized units like CBRN formations, Special Operations Command, Intelligence Agencies and their Paramilitary wing or even the Police Force and their Special Tactical Units have way more countermeasures, tools, resources that are not known to me. They are adequately prepared for a crisis of this level. That's excluding unknown compartmentalized task forces. Most of these capabilities are not transparent to the public for obvious reasons.
Moreover there are contractors in the public sector too, that have expertise in such emergencies and will be drawn to aid the military.
There's also the investigative element on the root cause and source of the crisis which will likely be spearheaded by a Joint Task Force of military and civilian counterparts. Something i have little exposure to so i can't explain much but it is part of protocol.
In the modern day setting, militaries don't operate alone, it's always a Joint Operation between the Military, Police, Gov & Civilian Agencies, various Intelligence Services and Contractors.
Contrary to what most think, the various agencies don't squabble with one another, at least not like in the movies. No matter who takes command, everyone will work together and won't deliberately shut out others or fight for control. You see a lot of friction between the different sub-factions in movies and books because the writer just wants drama.
In all honesty, a typical zombie apocalypse won't even be an issue. Unless it's an airborne Covid Zombie virus that also creates special infected that are built like a tank, runs like a cheetah, has adamantium claws, the strength of a few elephants and shoots out long range anti armor acid spits & projectiles. Or there are supernatural elements involved. Or we're invaded by Type III alien civilizations that mastered galactic travel, harnessed the power of black holes & dark matter, possesses wormhole & dimensional tech and has limited space-time manipulation capabilities.
