loginScreen.js

/**
 * Sample React Native App
 * https://github.com/facebook/react-native
 */
'use strict';

const React = require('react-native');
const FBSDKCore = require('react-native-fbsdkcore');
const FBSDKLogin = require('react-native-fbsdklogin');

var Parse = require('parse/react-native');
var ParseReact = require('parse-react/react-native');

Parse.initialize(
  '******',
  '******'
);

const {
  StyleSheet,
  Text,
  View,
  Component,
} = React;


const {
  FBSDKGraphRequest,
  FBSDKAccessToken,
} = FBSDKCore;

const {
  FBSDKLoginButton,
} = FBSDKLogin;

class LoginScreen extends Component {

  _onPressFBLoginButton(credentials) {

    // the timestamp needs to be reformatted for Parse http://stackoverflow.com/questions/12945003/format-date-as-yyyy-mm-ddthhmmss-sssz
    var expdate = new Date(credentials._expirationDate);
    expdate = expdate.toISOString();

    // these are the data from the successful FB login we will pass to Parse.FacebookUtils.logIn instead of null
    // based on https://github.com/ParsePlatform/ParseReact/issues/45#issuecomment-111063927
    let authData = {
      id: credentials.userID,
      access_token: credentials.tokenString,
      expiration_date: expdate
    };

    Parse.FacebookUtils.logIn(authData, {
      success: function(user) {
        if (!user.existed()) {
          alert("User signed up and logged in through Facebook!");
        } else {
          alert("User logged in through Facebook!");
        }
      },
      error: function(user, error) {
        console.log(user,error);
        alert("User cancelled the Facebook login or did not fully authorize.");
      }
    });
  }

  render() {
    return (
      <View style={styles.container}>
        <Text style={styles.welcome}>
          Log in
        </Text>
        <FBSDKLoginButton
          onLoginFinished={(error, result) => {
            if (error) {
              alert('Error logging in.');
            } else {
              if (result.isCancelled) {
                alert('Login cancelled.');
              } else {
                console.log(result);

                // we need to make one more request to get the token becase the token is not sent back in the login
                var fetchMeRequest = new FBSDKGraphRequest((error, result) => {
                  if (error) {
                    alert('Error making request.');
                  } else {
                    // Data from request is in result
                    FBSDKAccessToken.getCurrentAccessToken((token) => {
                      //console.log(token);
                      this._onPressFBLoginButton(token);
                    });

                  }
                }, '/me?fields=id,first_name,name,birthday,gender,email');
                // Start the graph request.
                fetchMeRequest.start();
              }
            }
          }}
          onLogoutFinished={() => alert('Logged out.')}
          readPermissions={['public_profile', 'email']}
          publishPermissions={[]}/>
      </View>
    );
  }
}

const styles = StyleSheet.create({
  container: {
    flex: 1,
    justifyContent: 'center',
    alignItems: 'center',
    backgroundColor: '#F5FCFF',
  },
  welcome: {
    fontSize: 20,
    textAlign: 'center',
    margin: 10,
  },
});

module.exports = LoginScreen;

this helps, thanks