グーグルマップAPIでポリラインの色を設定する条件を作成します

配列を処理して、データ内の2つのポイントのセットごとに個別のポリラインを作成し、各セグメントにそのエンドポイントの1つに関連付けられた色を割り当てる必要があります。

// only go to length - 1 or you will overrun the array
for (var i = 0; i < polyline_data.length - 1; i++) {
  // for each segment of two points
  var polylinePlanCoordinates = [];
  polylinePlanCoordinates.push(new google.maps.LatLng(polyline_data[i]['latitude'], polyline_data[i]['longitude']));
  polylinePlanCoordinates.push(new google.maps.LatLng(polyline_data[i + 1]['latitude'], polyline_data[i + 1]['longitude']));

  // create a polyline
  var path = new google.maps.Polyline({
    path: polylinePlanCoordinates,
    geodesic: true,
    strokeOpacity: 1.0,
    strokeWeight: 5
  });
  // set the color of the segment based on the lowest index point
  if (polyline_data[i]['kon_jem'] > 0 && polyline_data[i]['kon_jem'] < 3) {
    path.setOptions({
      strokeColor: '#ffffff'
    });
  } else if (polyline_data[i]['kon_jem'] > 3 && polyline_data[i]['kon_jem'] < 9) {
    path.setOptions({
      strokeColor: '#000000'
    });
  } else if (polyline_data[i]['kon_jem'] > 9) {
    path.setOptions({
      strokeColor: '#fff000'
    });
  }
  path.setMap(map);
}

概念実証フィドル

コードスニペット：

function initialize() {
  var map = new google.maps.Map(
    document.getElementById("map_canvas"), {
      center: new google.maps.LatLng(37.4419, -122.1419),
      zoom: 13,
      mapTypeId: google.maps.MapTypeId.ROADMAP
    });
  var bounds = new google.maps.LatLngBounds();
  for (var i = 0; i < polyline_data.length - 1; i++) {
    // for each segment of two points
    var polylinePlanCoordinates = [];
    polylinePlanCoordinates.push(new google.maps.LatLng(polyline_data[i]['latitude'], polyline_data[i]['longitude']));
    polylinePlanCoordinates.push(new google.maps.LatLng(polyline_data[i + 1]['latitude'], polyline_data[i + 1]['longitude']));

    // create a polyline
    var path = new google.maps.Polyline({
      path: polylinePlanCoordinates,
      geodesic: true,
      strokeOpacity: 1.0,
      strokeWeight: 5
    });
    bounds.extend(path.getPath().getAt(0));
    bounds.extend(path.getPath().getAt(1));

    if (polyline_data[i]['kon_jem'] > 0 && polyline_data[i]['kon_jem'] < 3) {
      path.setOptions({
        strokeColor: '#ffffff'
      });
    } else if (polyline_data[i]['kon_jem'] > 3 && polyline_data[i]['kon_jem'] < 9) {
      path.setOptions({
        strokeColor: '#000000'
      });
    } else if (polyline_data[i]['kon_jem'] > 9) {
      path.setOptions({
        strokeColor: '#fff000'
      });
    }
    path.setMap(map);

  }
  map.fitBounds(bounds);
}
google.maps.event.addDomListener(window, "load", initialize);
var polyline_data = [
  {latitude: 0, longitude: 0, kon_jem: 0},
  {latitude: 0.1, longitude: 0.2, kon_jem: 1},
  {latitude: 0.2, longitude: 0.1, kon_jem: 2},
  {latitude: 0.3, longitude: 0.2, kon_jem: 3},
  {latitude: 0.4, longitude: 0.1, kon_jem: 4},
  {latitude: 0.5, longitude: 0.2, kon_jem: 5},
  {latitude: 0.6, longitude: 0.1, kon_jem: 6},
  {latitude: 0.7, longitude: 0.2, kon_jem: 7},
  {latitude: 0.8, longitude: 0.1, kon_jem: 8},
  {latitude: 0.9, longitude: 0.3, kon_jem: 9},
  {latitude: 0.9, longitude: 0.1, kon_jem: 10},
  {latitude: 1.0, longitude: 0.1, kon_jem: 11},
  {latitude: 1.1, longitude: 0.2, kon_jem: 12},
  {latitude: 1.2, longitude: 0.1, kon_jem: 13},
  ];

html,
body,
#map_canvas {
  height: 100%;
  width: 100%;
  margin: 0px;
  padding: 0px
}

<script src="https://maps.googleapis.com/maps/api/js"></script>
<div id="map_canvas"></div>