How to style AlertDialog Actions in Flutter

Don't add button in actions of AlertDialog. As you can see.

_onSubmit(message) {
    if (message.isNotEmpty) {
      showDialog(
        context: context,
        barrierDismissible: false,
        builder: (BuildContext context) {
          return AlertDialog(
            title: Center(child: Text('Alert')),
            content: Row(
              mainAxisAlignment: MainAxisAlignment.center,
              crossAxisAlignment: CrossAxisAlignment.center,
              children : <Widget>[
                Expanded(
                  child: Text(
                    message,
                    textAlign: TextAlign.center,
                    style: TextStyle(
                      color: Colors.red,

                    ),
                  ),
                ),

         FlatButton(
                  child: Text('Cancel'),
                  onPressed: () {
                    Navigator.of(context).pop();
                  }),
              FlatButton(
                  child: Text('Ok'),
                  onPressed: () {
                    _inputTextController.clear();
                    Navigator.of(context).pop();
                  })
              ],
            ),
          );
        },
      );
    }
  }

Customize widget

Edit the the widget itself: Under the AlertDialog there is a ButtonBar widget where you can use alignment: MainAxisAlignment.spaceBetween to align the buttons correctly. See this answer for an example of a custom AlertDialog widget.

Own button row

You could also remove the buttons under actions and add an own custom Row with RaisedButtons in it, somehow like this:

Row (
    mainAxisAlignment: MainAxisAlignment.spaceBetween,
    children: <Widget>[
        RaisedButton(), // button 1
        RaisedButton(), // button 2
    ]
)

In your case you could add a Column around the Row in content and in there add your existing Row and the modified one you created from the above example.

Move buttons to content is a good solution.

showDialog(
              context: context,
              barrierDismissible: false,
              builder: (BuildContext context) {
                return AlertDialog(
                  title: Center(child: Text('Alert')),
                  content: Column(
                    mainAxisSize: MainAxisSize.min,
                    children: <Widget>[
                      Container(
                        child: Text(
                          "message",
                          textAlign: TextAlign.center,
                          style: TextStyle(
                            color: Colors.red,
                          ),
                        ),
                      ),
                      Row(
                        mainAxisAlignment: MainAxisAlignment.spaceBetween,
                        children: <Widget>[
                          FlatButton(
                              child: Text('Yes'),
                              onPressed: () {
                                Navigator.of(context).pop();
                              }),
                          FlatButton(
                              child: Text('No'),
                              onPressed: () {
                                Navigator.of(context).pop();
                              })
                        ])
                    ],
                  ),
                );
              });