Flutter: Right overflowed by 200 pixels

If by

All remaining chips should get displayed below to it

you mean that the Chips should wrap when there's no space left on the row then you should use the Wrap widget (Documentation) instead of Row. It automatically displays its children in multiple horizontal or vertical runs:

new Wrap(
  spacing: 8.0, // gap between adjacent chips
  runSpacing: 4.0, // gap between lines
  direction: Axis.horizontal, // main axis (rows or columns)
  children: <Widget>[
    new Chip(
      label: new Text('Chips11')
    ),new Chip(
      label: new Text('Chips12')
    ),new Chip(
      label: new Text('Chips13')
    ),new Chip(
      label: new Text('Chips14')
    ),new Chip(
      label: new Text('Chips15')
    ),new Chip(
      label: new Text('Chips16')
    )
  ],
)