Adding icon to left of DropDownButton (expanded) in flutter

There is no specific attribute for adding icon the way you want but you can always work around your code and find some tweaks. Use the following code which will place you Icon() on top of your DropDownButton() button.

@override
Widget build(BuildContext context) {
return Scaffold(
body: Stack(
  children: <Widget>[
    Container(
      decoration: BoxDecoration(
        color: Colors.white,
        boxShadow: [
          BoxShadow(
            color: Colors.grey,
            blurRadius: 20.0,
            spreadRadius: 0.5,
            offset: Offset(1.0, 1.0),
          ),
        ],
      ),
      padding: EdgeInsets.only(left: 44.0),
      margin: EdgeInsets.only(top: 64.0, left: 16.0, right: 16.0),
      child: DropdownButton(
        isExpanded: true,
        items: your_list.map(
          (val) {
            return DropdownMenuItem(
              value: val,
              child: Text(val),
            );
          },
        ).toList(),
        value: _currentSelectedItem,
        onChanged: (value) {
          setState(() {
            _currentSelectedItem = value;
          });
        },
      ),
    ),
    Container(
      margin: EdgeInsets.only(top: 80.0, left: 28.0),
      child: Icon(
        Icons.person,
        color: Colors.redAccent,
        size: 20.0,
      ),
    ),
  ],
),
  );
}

Use DropdownButtonFormField as it has decoration property. You can use prefixIcon attribute to set icon on left side.

Example:

DropdownButtonFormField<String>(
         decoration: InputDecoration(
         prefixIcon: Icon(Icons.person),
         ),
         hint: Text('Please choose account type'),
         items: <String>['A', 'B', 'C', 'D'].map((String value) {
         return DropdownMenuItem<String>(
         value: value,
         child: new Text(value),
       );
      }).toList(),
     onChanged: (_) {},
),

Result: