Listen for widget size changes.

main.dart

import 'package:flutter/foundation.dart';
import 'package:flutter/material.dart';
import 'package:flutter/scheduler.dart';
import 'package:flutter/widgets.dart';

/// There's an alternative and better way to achieve this by using RenderObject / CustomMultiChildLayout but I will not cover it here.

class MyTextInput extends StatefulWidget {
  @override
  _MyTextInputState createState() => _MyTextInputState();
}

class _MyTextInputState extends State<MyTextInput> {
  final ValueNotifier<double> _scrollViewPaddingNotifier = ValueNotifier(0);
  final GlobalKey _textFieldKey = GlobalKey();

  @override
  void initState() {
    SchedulerBinding.instance.addPostFrameCallback((_) {
      _updateScrollViewPadding();
    });
    super.initState();
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Stack(
        children: <Widget>[
          ValueListenableBuilder<double>(
            valueListenable: _scrollViewPaddingNotifier,
            builder: (BuildContext context, double paddingBottom, Widget child) {
              print('ScrollView padding: $paddingBottom');
              return ListView(
                reverse: true,
                children: [
                  Text('item 0'),
                  Text('item 1'),
                  Text('item 2'),
                ],
                padding: EdgeInsets.only(bottom: paddingBottom),
              );
            },
          ),
          Column(
            mainAxisAlignment: MainAxisAlignment.end,
            children: <Widget>[
              Container(
                color: Colors.greenAccent.withOpacity(0.5),
                child: NotificationListener<SizeChangedLayoutNotification>(
                  onNotification: (notification) {
                    print('notification: $notification');
                    _updateScrollViewPadding();
                    return true;
                  },
                  child: SizeChangedLayoutNotifier(
                    child: TextField(
                      key: _textFieldKey,
                      decoration: InputDecoration(
                        hintText: 'Type something...',
                        isDense: true,
                        border: InputBorder.none,
                      ),
                      maxLines: 4,
                      minLines: 1,
                    ),
                  ),
                ),
              ),
            ],
          ),
        ],
      ),
    );
  }

  void _updateScrollViewPadding() {
    final height = _textFieldKey.currentContext.size.height;
    SchedulerBinding.instance.addPostFrameCallback((_) {
      _scrollViewPaddingNotifier.value = height;
    });
  }
}