ReactNativeEventBindingTest.jsx

import React, { Component } from 'react';
import { Text, FlatList, View, StyleSheet, Button } from 'react-native';
import { Constants } from 'expo';

const TouchableTextConst = props => {
  console.log(`TouchableTextConst${props.id} rendered, callback (re)created :(`);
  const textPressed = () => {
    props.onPressItem(props.id);
  };
  
  return (
    <Text style={styles.item} onPress={textPressed}>{props.children}</Text>
  );
};

class TouchableTextClass extends React.PureComponent {
  constructor(props) {
    super(props);
    this.textPressed = this.textPressed.bind(this);
  }
  
  textPressed(){
    this.props.onPressItem(this.props.id);
  }

  render() {
    console.log(`TouchableTextClass${this.props.id} rendered, element only :)`);
    return (
      <Text style={styles.item} onPress={this.textPressed}>
        {this.props.children}
      </Text>
    );
  }
}

export default class App extends Component {
  constructor(props) {
    super(props);
    this.state = {
      clicks: 0,
    };

    //event binding in constructor for performance (happens only once)
    //see facebook advice:
    //https://facebook.github.io/react/docs/handling-events.html
    this.handlePress = this.handlePress.bind(this);
    this.increment = this.increment.bind(this);
  }

  increment() {
    const { clicks } = this.state;

    this.setState({
      clicks: clicks + 1,
    });
  }

  handlePress(id) {
    //Do what you want with the id
    console.log(`${id} pressed`);
  }

  render() {
    return (
      <View style={styles.container}>
        <Button onPress={this.increment} title={'Tap to re render'} />
        <Text>{this.state.clicks}</Text>
        <View style={styles.listsContainer}>
          <View>
            <Text>WithClassFLatList</Text>
            <FlatList
              data={[
                { id: 'WithClass1' },
                { id: 'WithClass2' },
                { id: 'WithClass3' },
                { id: 'WithClass4' },
                { id: 'WithClass5' },
              ]}
              renderItem={({ item }) => (
                <TouchableTextClass id={item.id} onPressItem={this.handlePress}>
                  {item.id}
                </TouchableTextClass>
              )}
            />
          </View>
          <View>
            <Text>WithConstFLatList</Text>
            <FlatList
              data={[
                { id: 'WithConst1' },
                { id: 'WithConst2' },
                { id: 'WithConst3' },
                { id: 'WithConst4' },
                { id: 'WithConst5' },
              ]}
              renderItem={({ item }) => (
                <TouchableTextConst id={item.id} onPressItem={this.handlePress}>
                  {item.id}
                </TouchableTextConst>
              )}
            />
          </View>
        </View>
      </View>
    );
  }
}

const styles = StyleSheet.create({
  container: {
    flex: 1,
    alignItems: 'center',
    justifyContent: 'center',
    paddingTop: Constants.statusBarHeight,
    backgroundColor: '#ecf0f1',
  },
  listsContainer: {
    marginTop: 25,
    flex: 1,
    flexDirection: 'row',
  },
  item: {
    margin: 5,
    padding: 15,
    fontSize: 18,
    fontWeight: 'bold',
    textAlign: 'center',
    color: '#34495e',
    backgroundColor: 'yellow',
  },
});

Some references:
Different types of event bindings and which one to choose (with a button)
React Native Handling Events Doc
React Native FlatList Doc
Event handlers and Functional Stateless Components
React Binding Patterns: 5 Approaches for Handling this