Add this to your package's pubspec.yaml file:

dependencies:
 location: ^3.0.0

Android

 特に設定は必要ない

iOS 
ios/Runner/Info.plistに以下の項目を追加

<key>NSLocationAlwaysUsageDescription</key>            
<string>Your location is required for this app</string>
<key>NSLocationWhenInUseUsageDescription</key>         
<string>Your location is required for this app</string>

スマホの位置情報がオンになっているか、アプリが位置情報にアクセスできるかの確認

Future<bool> checkLocation() async {
 Location location = new Location();
 bool _serviceEnabled;
 PermissionStatus _permissionGranted;
 _serviceEnabled = await location.serviceEnabled();
 if (!_serviceEnabled) {
   _serviceEnabled = await location.requestService();
   if (!_serviceEnabled) {
     return false;
   }
 }
 _permissionGranted = await location.hasPermission();
 if (_permissionGranted == PermissionStatus.denied) {
   _permissionGranted = await location.requestPermission();
   if (_permissionGranted != PermissionStatus.granted) {
     return false;
   }
 }
 return true;
}

情報取得

Future<List<String>> getLocation() async {
 Location location = new Location();
 LocationData _locationData = await location.getLocation();
 return [
   _locationData.longitude.toString(),
   _locationData.latitude.toString()
 ];
}

参考