Positioning a Widget in the end of the Row widget

you can add Spacer(), above the widget you want to put at the end.

One solution is to use the Spacer widget to fill up the space

https://docs.flutter.io/flutter/widgets/Spacer-class.html

    Row(
            mainAxisAlignment: MainAxisAlignment.start, //change here don't //worked
            crossAxisAlignment: CrossAxisAlignment.center,
            children: <Widget>[
              Container(
                margin:
                    EdgeInsets.only(left: 8.0, top: 8.0, bottom: 8.0, right: 12.0),
                width: 15.0,
                height: 15.0,
                decoration: BoxDecoration(
                    color: Colors.red, borderRadius: BorderRadius.circular(40.0)),
              ),
              Column(
                crossAxisAlignment: CrossAxisAlignment.start,
                children: <Widget>[
                  Text(
                    "task.title",
                    style: TextStyle(
                        color: Colors.black,
                        fontSize: 19.0,
                        fontWeight: FontWeight.bold),
                  ),
                  Text(
                    'Duration: ${somenum}',
                    style: TextStyle(color: Colors.black, fontSize: 14.0),
                  )
                ],
              ),
              new Spacer(), // I just added one line
              Icon(Icons.navigate_next, color: Colors.black) // This Icon
            ],
          ),

Here is what happens if you add it to the beginning of the Row.