最先看网上说只启动一次需要修改C++代码，参考文档如下：
Run only single instance of flutter desktop application

代码内容如下：

HANDLE hMutexHandle=CreateMutex(NULL, TRUE, L"my.mutex.name");
HWND handle=FindWindowA(NULL, "Test Application");

  if (GetLastError() == ERROR_ALREADY_EXISTS)
  {
     WINDOWPLACEMENT place = { sizeof(WINDOWPLACEMENT) };
         GetWindowPlacement(handle, &place);
         switch(place.showCmd)
         {
              case SW_SHOWMAXIMIZED:
                  ShowWindow(handle, SW_SHOWMAXIMIZED);
                  break;
              case SW_SHOWMINIMIZED:
                  ShowWindow(handle, SW_RESTORE);
                  break;
              default:
                  ShowWindow(handle, SW_NORMAL);
                  break;
          }
          SetWindowPos(0, HWND_TOP, 0, 0, 0, 0, SWP_SHOWWINDOW | SWP_NOSIZE | SWP_NOMOVE);
          SetForegroundWindow(handle);
          return 0;
  }

操作那么多实在看不懂，毕竟没有写过C++。通过继续努力寻找，终于在现有的插件中，有这样一款插件可以实现。

windows_single_instance

Add WidgetsFlutterBinding.ensureInitialized(); to the start of your apps main function.
Add the async modifier to your apps main function.
Add a call to WindowsSingleInstance.ensureSingleInstance(), passing the apps startup args, a custom app string unique to your app (a-z, 0-9, _ and - only), and an optional callback function.

使用非常简单

void main(List<String> args) async {
    WidgetsFlutterBinding.ensureInitialized();
    //单实例启动
    await WindowsSingleInstance.ensureSingleInstance(args, "app_id",
        onSecondWindow: (args) async {
        if (await windowManager.isMinimized()) {
            windowManager.restore();
        }
        windowManager.focus();
    });
    runApp(const MyApp());
}

以上就可以实现单实例启动了。