Positioning a Widget in the end of the Row widget

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.