Place button on top of joining lines of two containers

You can use Column with Flexible to set ratios between two Container(Blue and White in your example).

Put the button between containers and use Transform.translate to offset it for half it's height in a negative direction. This will put it on top of the blue Conainer.

Working example

import 'package:flutter/material.dart';

void main() => runApp(MyApp());

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) => MaterialApp(home: MyPage());
}

class MyPage extends StatefulWidget {
  @override
  _MyPageState createState() => _MyPageState();
}

class _MyPageState extends State<MyPage> with WidgetsBindingObserver {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: SafeArea(
        child: _buildColumn(),
      ),
    );
  }

  Widget _buildColumn() => Column(
        crossAxisAlignment: CrossAxisAlignment.stretch,
        children: [
          // First blue container
          _buildTopContainer(),
          // Button with offset
          _buildMidContainerWithButton(),
          // Bottom white container
          _buildBottomContainer(),
        ],
      );

  Widget _buildTopContainer() => Flexible(
        flex: 10,
        child: Container(
          color: Colors.blue[900],
          child: Column(
            mainAxisAlignment: MainAxisAlignment.center,
            children: [
              Text(
                'Top container',
                style: TextStyle(
                  fontSize: 17.0,
                  fontWeight: FontWeight.w600,
                  color: Colors.white,
                ),
              ),
            ],
          ),
        ),
      );

  Widget _buildMidContainerWithButton() {
    final buttonHeight = 50.0;
    return Stack(
      children: [
        // Use same background color like the second container
        Container(height: buttonHeight, color: Colors.white),
        // Translate the button 
        Transform.translate(
          offset: Offset(0.0, -buttonHeight / 2.0),
          child: Center(
            child: GestureDetector(
              onTap: () { /* do stuff */ },
              child: Container(
                height: buttonHeight,
                decoration: BoxDecoration(
                  color: Colors.orange[400],
                  borderRadius: BorderRadius.circular(buttonHeight / 2.0),
                  boxShadow: [
                    BoxShadow(
                      blurRadius: 16.0,
                      offset: Offset(0.0, 6.0),
                      color: Colors.black.withOpacity(0.16),
                    ),
                  ],
                ),
                padding: const EdgeInsets.fromLTRB(24.0, 3.0, 24.0, 0.0),
                child: Row(
                  mainAxisSize: MainAxisSize.min,
                  children: [
                    Icon(
                      Icons.photo_camera_outlined,
                      size: 20.0,
                      color: Colors.white,
                    ),
                    Padding(
                      padding: const EdgeInsets.only(left: 8.0),
                      child: Text(
                        'Use camera',
                        style: TextStyle(
                          fontSize: 17.0,
                          fontWeight: FontWeight.w600,
                          color: Colors.white,
                        ),
                      ),
                    ),
                  ],
                ),
              ),
            ),
          ),
        ),
      ],
    );
  }

  Widget _buildBottomContainer() => Flexible(
        flex: 5,
        child: Container(
          color: Colors.white,
          child: Column(
            mainAxisAlignment: MainAxisAlignment.center,
            children: [
            Text(
              'Bottom container',
              style: TextStyle(
                fontSize: 17.0,
                fontWeight: FontWeight.w600,
                color: Colors.black54,
              ),
            ),
          ]),
        ),
      );
}

Result