Uncrackable, I'd say, unless an early newspaper text or something similar turns up.

Of course, I've looked as best I can and found nothing. But not all newspapers broadsides, or handwritten manuscripts survive.

By the way, the very latest online revision of Oxford, from 2019, gives an example of "firing line" from 1854 and another from 1859.

(But mine's still earlier. Heh heh.)

More seriously it's the sort of arcane term that would most likely have been used by someone with some kind of military background, even if it was only drilling on the town square with a local militia.

Which isn't terribly helpful.