Yahweh promises Israel that he will raise a banner around which the exiled people of God will gather (Isaiah 11:12), but this gathering is also a gathering for battle (11:14-15). At the beginning of the oracle against Babylon, Yahweh again promises to raise a banner, and again it is a military standard, mustering God’s holy warriors (13:2-3)
Later in chapter 13, Isaiah explicitly mentions the Medes who are stirred up against Babylon (v. 17), and perhaps Yahweh’s “holy ones” and “mighty men” are the Medes. But it would be an odd way to describe a Gentile army. More likely, the consecrated ones are the people of Israel, gathered as the remnant to the banner of Yahweh, the banner that is the Branch and Root of Jesse (11:1, 10). They are the agents of the destruction of Babylon, just as Israel in Egypt were the “hosts” of Yahweh, even though they didn’t do much fighting (as Toby Sumpter has pointed out).
The gathered exiles are in Babylon as a fifth column, agents of Yahweh’s anger. Holy warriors and mighty men are called “to My anger” or “to My nose.” Even before the Medes appear to scatter Babylon, Israel’s people has become the fire that flames from the burning nose of Yahweh.