Symbolism, Imagery, Allegory
Okay, you just know that the angel of death is up to no good. It's the freakin' angel of death.
The angel appears just after Salomé introduces herself to Jokanaan (dum dum dummm). Oddly enough, his appearance actual surprises the prophet, the very one who usually forecasts these sorts of things. "Get thee behind me!" he says. "I hear in the palace the beating of the wings of the angel death" (40).
At this point, the angel's allegiance isn't clear—John's exclamation is reminiscent of Jesus' own "Get behind me, Satan!"— but he immediately clarifies the situation:
JOKANAAN: Angel of the Lord God, what doest thou here with thy sword? Whom seekest thou in this palace? The day of him who shall die in the robe of silver has not yet come. (42)
The angel is an agent of God and a freaky manifestation of God's judgment. As far as Jokanaan can tell, though, he's showed up a little early. And he chooses an unlikely character to visit: Herod. Throughout the play, Herod feels a cold wind and hears "the beating of vast wings" (91). This raises the question: why does he make himself known to Herod when Herod is not directly touched by death?
Sure, he orders the execution of John the Baptist and Salomé, but you could argue that in the first case he has to keep his oath, and that in the second Salomé deserves to die for what she does (make out with a severed head, ew, ew, ew).
You could try out any number of theories—maybe it's because Herod is very prone to taking things as omens?—but, no matter how you slice it, the angel's appearance fits in with a larger pattern: he connects the events of the play to the events which Jokanaan prophesies. Yup: doom n' gloom.