How to remove a item/index from a FlatList in react native?

General pattern is to pass a uniquely identifiable id (key, index, etc...) to your delete handler and filter your data on values that don't equal that key. This returns a new array without that entry to store in state.

deleteItemById = id => {
  const filteredData = this.state.data.filter(item => item.id !== id);
  this.setState({ data: filteredData });
}

render() {
  ...

  return (   
    <FlatList 
      data={data} // Assuming this is `this.state.data`
      keyExtractor={({item}) => item.id}                
      renderItem={({item}) => (
        <View style={styles.container}>
          <SwipeView
            ...
            onSwipedLeft={() => this.deleteItemById(item.id)}
            ...
          />
        </View>  
      )}
    />
  );
}

Using a curried handler. This saves using an anonymous callback by setting the callback to be an event handler with the id enclosed in the function scope.

deleteItemById = id => () => {
  const filteredData = this.state.data.filter(item => item.id !== id);
  this.setState({ data: filteredData });
}

render() {
  ...

  return (   
    <FlatList 
      data={data} // Assuming this is `this.state.data`
      keyExtractor={({item}) => item.id}                
      renderItem={({item}) => (
        <View style={styles.container}>
          <SwipeView
            ...
            onSwipedLeft={this.deleteItemById(item.id)}
            ...
          />
        </View>  
      )}
    />
  );
}

Pass an Id of the item to onSwipeLeft={this.deleteItem(item.id)} and update the data using setState.

state = {
    data: [{
      title: 'Hello world',
      id: 'hello'
    },{
      title: 'World says hello',
      id: 'say'
    }]
}

deleteItem = (id) => {

   this.setState({
    data: this.state.data.filter(item => item.id !== id)
   })

}