Certainly, like 'PieToro' says, the Armada is getting raw materials from their land-destroying machine, as we saw in Granchia. But they essentially have control of Valencia, a world of long-standing wealth, art, and scholarship. So while they do not value art themselves, I'm sure Kane is clever enough to realize that there would be many buyers throughout the Spiral for Valencian art and art collections. So, essentially, they can loot their own country for considerable gain (as well as looting the Azteca tombs of Skull Island), and that allows them to bring in more construction materials (or bribe informants and allies, offer a large reward for the capture of a certain annoying pirate... whatever they wish)
Nor is metal the only thing that goes into Armada construction (and their constructs, for that matter). I see wood graining (and quite beautiful design) in Beachhead. Blind Mew at one point indicated that the Armada constructs are not merely metal, but also light wood and wire (which is metal, I suppose, just very light and thin). Thus the Armada soldiers are light, flexible, and graceful (well, except for huge ones like the Dragoons!) as opposed to the clunky Marleybonean golems, which seem to be largely made of metal.