To find the resolution of several monitors, you can scroll the Screen.screens array, and then get the bounding box of each monitor screen. Normally, AIR counts from left to right (0 indexes the right monitor), but I have not tested this with every monitor configuration.
import flash.display.Screen;
for (var i: int = 0; i <Screen.screens.length; i ++)
{
var x = Screen.screens [i] .bounds.left;
var y = 0;
var width = Screen.screens [i] .bounds.width;
var height = Screen.screens [i] .bounds.height;
}
source share