According to Revelation 2, the false prophetess Jezebel has children, her disciples. And these too are going to suffer the judgment of Jesus. Jesus is going to “kill them with death” (apokteno en thanato). The doubling is for emphasis, and reminds us of the “dying you will die” of Genesis 2-3: They will surely die when Jesus comes to the church, like Yahweh coming into the garden in the Spirit of the day.
The double death is also an anticipation of the “second death” that is mentioned later in Revelation. The children of the harlot are not simply going to die, but to go into the late of fire, the second death.