How to apply flex in flutter

Expanded is Similar to Flex and supports adding flex,

You can wrap your children with Expanded and give flex as below

Updated Code :

Container(
  child: new Row(
    children: <Widget>[
      new Expanded ( 
        flex:1,
        child : Column(
        children: <Widget>[new Text("Hello World")],
      ),),
      new Expanded( 
        flex :2,
        child: Column(
        children: <Widget>[
          new Text(
              "This is a long text this is a long test this is This is a long text this is a long test this is This is a long text this is a long test this is This is a long text this is a long test this is This is a long text this is a long test this is This is a long text this is a long test this is ")
        ],
      ),)
    ],
  ),
)

Expanded : A widget that expands a child of a Row, Column, or Flex so that the child fills the available space.

You can read more at official docs here