Code:
new Container(
          alignment: FractionalOffset.center,
          child: new Row(
            mainAxisAlignment: MainAxisAlignment.spaceEvenly,
             
        Removing Space-:
new Row(
            mainAxisAlignment: MainAxisAlignment.center,
            children: <Widget>[
              GestureDetector(
                child: new Text('Don\'t have an account?',
                    style: new TextStyle(color: Color(0xFF2E3233))),
                onTap: () {},
              ),
              GestureDetector(
                onTap: (){},
                  child: new Text(
                'Register.',
                style: new TextStyle(
                    color: Color(0xFF84A2AF), fontWeight: FontWeight.bold),
              ))
            ],
          ),
OR
GestureDetector(
            onTap: (){},
            child: new Row(
              mainAxisAlignment: MainAxisAlignment.center,
              children: <Widget>[
                new Text('Don\'t have an account?',
                    style: new TextStyle(color: Color(0xFF2E3233))),
                new Text(
                  'Register.',
                  style: new TextStyle(
                  color: Color(0xFF84A2AF), fontWeight: FontWeight.bold),
                )
              ],
            ),
          ),
You can use Spacers if all you want is a little bit of spacing between items in a row. The example below centers 2 Text widgets within a row with some spacing between them.
Spacer creates an adjustable, empty spacer that can be used to tune the spacing between widgets in a Flex container, like Row or Column.
In a row, if we want to put space between two widgets such that it occupies all remaining space.
    widget = Row (
    children: <Widget>[
      Spacer(flex: 20),
      Text(
        "Item #1",
      ),
      Spacer(),  // Defaults to flex: 1
      Text(
        "Item #2",
      ),
      Spacer(flex: 20),
    ]
  );