I've tried flutter_reorderable_list and dragable_flutter_list but none of them worked properly - there was some unwanted artifacts during dragging.
So I've tried to make own solution:
ListView.builder(
  itemBuilder: (context, index) => buildRow(index),
  itemCount: trackList.length,
),
Widget buildRow(int index) {
  final track = trackList[index];
  ListTile tile = ListTile(
    title: Text('${track.getName()}'),
  );
  Draggable draggable = LongPressDraggable<Track>(
    data: track,
    axis: Axis.vertical,
    maxSimultaneousDrags: 1,
    child: tile,
    childWhenDragging: Opacity(
      opacity: 0.5,
      child: tile,
    ),
    feedback: Material(
      child: ConstrainedBox(
        constraints:
            BoxConstraints(maxWidth: MediaQuery.of(context).size.width),
        child: tile,
      ),
      elevation: 4.0,
    ),
  );
  return DragTarget<Track>(
    onWillAccept: (track) {
      return trackList.indexOf(track) != index;
    },
    onAccept: (track) {
      setState(() {
        int currentIndex = trackList.indexOf(track);
        trackList.remove(track);
        trackList.insert(currentIndex > index ? index : index - 1, track);
      });
    },
    builder: (BuildContext context, List<Track> candidateData,
        List<dynamic> rejectedData) {
      return Column(
        children: <Widget>[
          AnimatedSize(
            duration: Duration(milliseconds: 100),
            vsync: this,
            child: candidateData.isEmpty
                ? Container()
                : Opacity(
                    opacity: 0.0,
                    child: tile,
                  ),
          ),
          Card(
            child: candidateData.isEmpty ? draggable : tile,
          )
        ],
      );
    },
  );
}
I guess, this is not the best solution, and I'm maybe will change it further, but for now it works quite well