How to justify (left, right, center) each child independently?

One way is to use nested View (flex containers) for 3 different regions and set flex:1 to left and right region

<View style={styles.navBar}>
  <View style={styles.leftContainer}>
    <Text style={[styles.text, {textAlign: 'left'}]}>
      {'<'}
    </Text>
  </View>
  <Text style={styles.text}>
    Fitness & Nutrition Tracking
  </Text>
  <View style={styles.rightContainer}>
    <View style={styles.rightIcon}/>
  </View>
</View>

const styles = StyleSheet.create({
  navBar: {
    height: 60,
    flexDirection: 'row',
    justifyContent: 'space-between',
    alignItems: 'center',
    backgroundColor: 'blue',
  },
  leftContainer: {
    flex: 1,
    flexDirection: 'row',
    justifyContent: 'flex-start',
    backgroundColor: 'green'
  },
  rightContainer: {
    flex: 1,
    flexDirection: 'row',
    justifyContent: 'flex-end',
    alignItems: 'center',
    backgroundColor: 'red',
  },
  rightIcon: {
    height: 10,
    width: 10,
    resizeMode: 'contain',
    backgroundColor: 'white',
  }
});