参考以下示例代码：

import 'package:intl/intl.dart';
import 'package:intl/date_symbol_data_local.dart';

void main() {
  initializeDateFormatting();

  //今天日期为2020-11-20

  print(DateFormat('EEE',"en_US").format(DateTime.now())); //Fri
  print(DateFormat('EEEE',"en_US").format(DateTime.now())); //Friday

  print(DateFormat('MM',"en_US").format(DateTime.now())); //11
  print(DateFormat('MMM',"en_US").format(DateTime.now())); //Nov
  print(DateFormat('MMMM',"en_US").format(DateTime.now())); //November


  //指定locale为zh_CN
  print(DateFormat('EEE',"zh_CN").format(DateTime.now())); //周五
  print(DateFormat('EEEE',"zh_CN").format(DateTime.now())); //星期五

  print(DateFormat('MM',"zh_CN").format(DateTime.now())); //11
  print(DateFormat('MMM',"zh_CN").format(DateTime.now())); //11月
  print(DateFormat('MMMM',"zh_CN").format(DateTime.now()));//十一月

}

以上为转载内容
其实Dart提供了DateTime.weekday函数，可以直接获取星期例：

//声明星期变量
var weekday = [" ", "星期一", "星期二", "星期三", "星期四", "星期五", "星期六", "星期日"];`
//变量直接调用日期函数weekday
weekday[DateTime.weekday];