How to draw a route on OSM on flutter App

I have create a component to display OpenStreetMap (OSM) on the view.

Question: How can I draw a static route on the map.

It should look like the following map I captured from GoogleMap.

What I have done so far. I created a view to show map.

import 'package:flutter/material.dart';
import 'package:flutter_map/flutter_map.dart';
import 'package:latlong/latlong.dart';

class TrailMapPage extends StatefulWidget {
  @override
  _TrailMapPageState createState() => _TrailMapPageState();
}

class _TrailMapPageState extends State<TrailMapPage> {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(title: Text("TrailMapPage")),
      body: _map(context),
    );
  }

  Widget _map(BuildContext context) {
    return new FlutterMap(
      options: MapOptions(
        center: LatLng(22.3193, 114.1694),
        zoom: 13.0,
      ),
      layers: [
        new TileLayerOptions(
            urlTemplate: "https://{s}.tile.openstreetmap.org/{z}/{x}/{y}.png",
            subdomains: ['a', 'b', 'c']),
        new MarkerLayerOptions(
          markers: [
            new Marker(
              width: 80.0,
              height: 80.0,
              point: new LatLng(51.5, -0.09),
              builder: (ctx) => new Container(
                child: new FlutterLogo(),
              ),
            ),
          ],
        ),
      ],
    );
  }
}