Flutter row place one item at start and other item in the middle

You could use the Spacer widget to fill available space in the row:

void main() => runApp(App());

class App extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: Scaffold(
        body: Center(
          child: Padding(
            padding: const EdgeInsets.all(8.0),
            child: SpacedRow(),
          ),
        ),
      ),
    );
  }
}

class SpacedRow extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Row(
      children: <Widget>[
        Container(width: 50, height: 50, color: Colors.red),
        Spacer(),
        Container(width: 50, height: 50, color: Colors.yellow),
        Spacer(),
      ],
    );
  }
}

Produces:

Though Jordan's answer achieved what the question mentioned, the yellow block does not look exactly center. I tried something like following

Stack(
          children: <Widget>[
            Row(
              mainAxisAlignment: MainAxisAlignment.center,
              mainAxisSize: MainAxisSize.max,
              children: <Widget>[
                Image.asset(
                  "images/toolbar_logo.webp",
                  width: 80,
                  height: 50,
                ),
              ],
            ),
            IconButton(
              icon: Icon(Icons.navigation),
              onPressed: () {},
              iconSize: 20,
            ),
          ],
        ),