Flutter Text Field: How to add Icon inside the border

Edited Answer

Updating answer as my original answer doesn’t actually cover the original context of the question.

You can use the prefixIcon in the TextField or in the TextFormField to get some widget as a leading in your TextField.

Example

    TextField(
//    ...,other fields
      decoration: InputDecoration(
        prefixIcon: prefixIcon??Icon(Icons.done),
      ),
    ),

PS: Do not get confuse between prefixIcon and prefix as this two
are different things.
https://api.flutter.dev/flutter/material/InputDecoration/prefix.html

Also if you want to achieve something like floating app bar then you can refer to my original answer.

Original answer

You can use my Flutter package to implement Floating AppBar in your application.

You need to add below package in your pub.

rounded_floating_app_bar: ^0.1.0

run $ flutter packages get from the command line.

Now in your Dart code, you can use:

import 'package:rounded_floating_app_bar/rounded_floating_app_bar.dart';
...
NestedScrollView(
  headerSliverBuilder: (context, isInnerBoxScroll) {
    return [
      RoundedFloatingAppBar(
        floating: true,
        snap: true,
        title: TextField(
          decoration: InputDecoration(
            prefixIcon: Icon(Icons.search),
            border: InputBorder.none,
          ),
        ),
      ),
    ];
  },
  body: Container(),
),

Output: