For me it's very strange usage of json file. But, to make it work I'd change json file to:
{
"lineformap": "[new google.maps.LatLng(52.25602231800669, 6.160540580749512),new google.maps.LatLng(52.25543780780041, 6.1602723598480225),new google.maps.LatLng(52.255818725438296, 6.160014867782593)]"
}
and
var flightPlanCoordinates = [
itemb.lineformap
];
to
var flightPlanCoordinates = eval(itemb.lineformap);
to get polyline.