React Native Text color not working

The flag variable is not in your component state, so the component will not re-render when it changes.

Put it in your component state instead and toggle it with setState and it will work.

class MyTest extends Component {
  state = { flag: true };

  changeColor = () => {
    this.setState(previousState => {
      return { flag: !previousState.flag };
    });
  };

  render() {
    return (
      <View style={styles.container}>
        <TouchableOpacity
          style={{ flex: 1, backgroundColor: "#888888", margin: 20 }}
          onPress={this.changeColor}
        >
          <Text style={{ color: this.state.flag ? "red" : "blue" }}>One</Text>
        </TouchableOpacity>
      </View>
    );
  }
}