Flutter divider widget not appearing

You could remove Row, then Column would take all available space and Divider would have width.

@override
Widget build(BuildContext context) {
  return new Padding(
    padding: const EdgeInsets.only(
        top: 16.0, bottom: 16.0, left: 12.0, right: 12.0),
    child: new Card(
      child: new Column(
        mainAxisSize: MainAxisSize.min,
        children: <Widget>[
          new Padding(
            padding: const EdgeInsets.only(top: 22.0, bottom: 8.0),
            child: new Text("Administrative",
                style: new TextStyle(
                    color: new Color.fromARGB(255, 117, 117, 117),
                    fontSize: 32.0,
                    fontWeight: FontWeight.bold)),
          ),
          new Divider(
            color: Colors.red,
          ),
          new Text("text")
        ],
      ),
    ),
  );
}

To make custom divider you could check implementation of Divider and adjust it. E.g. replace Divider with

new SizedBox(
  height: 10.0,
  child: new Center(
    child: new Container(
      margin: new EdgeInsetsDirectional.only(start: 1.0, end: 1.0),
      height: 5.0,
      color: Colors.red,
    ),
  ),
)