I've never heard of any militia unit carrying a Confederate national flag. If anything, it makes more sense for a company organized under state authority to carry a state flag.

Rather than being dressed as civilians, these men appear to be wearing matching sets of clothing. That's peculiar for most Civil War home guard units. Neckties were much larger during the late 1850s and early 1860s. Much smaller bowties (as seen in this image) came into vogue during the years after the war. The neatly trimmed beards and moustaches seen on several men look like the styles popular among older men during the 1890s and later.

As you mentioned, there's no evidence of military accoutrements or equipment. Where are the bayonets carried? What about cartridge and cap boxes, haversacks and canteens?