You would first need to create the actual style object via GEPlugin.createStyle()
before you can use it.
There are a few errors in your code. The lines
lineStringPlaceMark.setStyleSelector(m_ge.createStyle("").getLineStyle());
and
var lineStyle = m_ge.createStyle("").getLineStyle();
looking at it you would need to do something like.
var lineStringPlaceMark = m_ge.createPlacemark(string.Empty);
var lineString = m_ge.createLineString(string.Empty);
lineStringPlaceMark.setGeometry(lineString);
lineString.setExtrude(5);
lineString.setTessellate(500);
lineString.setAltitudeOffset(5);
lineString.setAltitudeMode(m_ge.ALTITUDE_RELATIVE_TO_GROUND);
for (int x = 0; x < arraylat.Length; x++)
{
lineString.getCoordinates().pushLatLngAlt(
Convert.ToDouble(arraylat[x]),
Convert.ToDouble(arraylong[x]), 0);
}
// we know the placemark has no style, so create one for it
lineStringPlaceMark.setStyleSelector(m_ge.createStyle(string.Empty));
// now you can access the style object
var lineStyle = lineStringPlaceMark.getStyleSelector().getLineStyle();
lineStyle.setWidth(100);
lineStyle.getColor().set("9900ffff");
m_ge.getFeatures().appendChild(lineStringPlaceMark);
You could also make a simple static method that returns the style selector for any feature, creating it if it doesn't exist.
// getStyleSelector wrapper, creates a style object if non is present
static dynamic GetStyleSelector(dynamic ge, dynamic feature) {
if(null == feature.getStyleSelector()) {
feature.setStyleSelector(ge.createStyle(string.Empty));
}
return feature.getStyleSelector();
}