You need another google.maps.Polyline()
...
var flightPlanCoordinates = [
new google.maps.LatLng(37.772323, -122.214897),
new google.maps.LatLng(21.291982, -157.821856),
new google.maps.LatLng(-18.142599, 178.431),
new google.maps.LatLng(-27.46758, 153.027892)
];
var flightPath = new google.maps.Polyline({
path: flightPlanCoordinates,
strokeColor: '#FF0000',
strokeOpacity: 1.0,
strokeWeight: 2
});
var flightPlanCoordinates2 = [
new google.maps.LatLng(37.772323, -122.214897),
new google.maps.LatLng(-27.46758, 153.027892)
];
var flightPath2 = new google.maps.Polyline({
path: flightPlanCoordinates2,
strokeColor: '#FF00FF',
strokeOpacity: 1.0,
strokeWeight: 2
});
flightPath.setMap(map);
flightPath2.setMap(map);
...