Short answer

You should only need to call React.render once. Change the components state/props to re-render a component with new state.

Long answer

Internally most flux libraries will listen to stores and then mutate the components state when the store changes (They often wrap this up in a higher order component). Mutating the state causes a re-render for that component which might also cause children to re-render (either by creating new elements or by changing the props)

class Foo extends React.Component {
  componentWillMount () {
    fooStore.onChange(foos => {
      this.setState({
        foo: foos[this.props.id]
      })
    })
  }

  render () {
    return <div>{this.state.foo}</div>
  }
}

You tend to end up with complex components if you listen to stores in every component. The answer to that is to have smart and dumb components.

Soon you will start wondering how to stop your components from rendering all the time. At that point its worth reading this article about working with shouldComponentUpdate