Well, the idea there is that they aren't actually making the muzzle loaders. There are God only knows how many of those things kicking about. I own a couple myself. Well, one is a cap and ball, as opposed to a flintlock, but you take my meaning. You can buy a brand new one anytime you want.
I actually buy the premise of going back to black powder weapons. All you need is lead and powder, which are easy. The machining and chemistry to produce brass casings, percussion primers, and jacketed bullets isn't something that would be reinvented at a 19th century level after so little time (and widespread societal collapse). We've frankly lost our ability to quickly rebuild a steam powered industry. The pre-electricity knowledge base is simply dead. We'd literally have to reinvent the steam engine at that scale. Only place where steam is still widely used is power plants.
Give them another 20 years or so, and they'd probably get their legs back under them to that extent. Pretty sure with only a decade going buy its still back-to-survival more than anything.
The writing on that show is pretty lazy though. Poorly written villains. Clunky dialogue.