сохранить изображение в галерею после снятия с камеры

Вы можете использовать пакет gallery_saver https://pub.dev/packages/gallery_saver
Получить изображение с ImagePicker и сохраните с помощью GallerySaver.saveImage

фрагмент кода

void _takePhoto() async {
    ImagePicker.pickImage(source: ImageSource.camera)
        .then((File recordedImage) {
      if (recordedImage != null && recordedImage.path != null) {
        setState(() {
          firstButtonText = 'saving in progress...';
        });
        GallerySaver.saveImage(recordedImage.path, albumName: albumName)
            .then((bool success) {
          setState(() {
            firstButtonText = 'image saved!';
          });
        });
      }
    });
  }

демонстрация

полный код

import 'dart:io';

import 'package:flutter/material.dart';
import 'package:gallery_saver/gallery_saver.dart';
import 'package:image_picker/image_picker.dart';

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

class MyApp extends StatefulWidget {
  @override
  _MyAppState createState() => _MyAppState();
}

class _MyAppState extends State<MyApp> {
  String firstButtonText = 'Take photo';
  String secondButtonText = 'Record video';
  double textSize = 20;
  String albumName ='Media';

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
        home: Scaffold(
      body: Container(
        color: Colors.white,
        child: Column(
          children: <Widget>[
            Flexible(
              flex: 1,
              child: Container(
                child: SizedBox.expand(
                  child: RaisedButton(
                    color: Colors.blue,
                    onPressed: _takePhoto,
                    child: Text(firstButtonText,
                        style:
                            TextStyle(fontSize: textSize, color: Colors.white)),
                  ),
                ),
              ),
            ),
            Flexible(
              child: Container(
                  child: SizedBox.expand(
                child: RaisedButton(
                  color: Colors.white,
                  onPressed: _recordVideo,
                  child: Text(secondButtonText,
                      style: TextStyle(
                          fontSize: textSize, color: Colors.blueGrey)),
                ),
              )),
              flex: 1,
            )
          ],
        ),
      ),
    ));
  }

  void _takePhoto() async {
    ImagePicker.pickImage(source: ImageSource.camera)
        .then((File recordedImage) {
      if (recordedImage != null && recordedImage.path != null) {
        setState(() {
          firstButtonText = 'saving in progress...';
        });
        GallerySaver.saveImage(recordedImage.path, albumName: albumName)
            .then((bool success) {
          setState(() {
            firstButtonText = 'image saved!';
          });
        });
      }
    });
  }

  void _recordVideo() async {
    ImagePicker.pickVideo(source: ImageSource.camera)
        .then((File recordedVideo) {
      if (recordedVideo != null && recordedVideo.path != null) {
        setState(() {
          secondButtonText = 'saving in progress...';
        });
        GallerySaver.saveVideo(recordedVideo.path, albumName: albumName)
            .then((bool success) {
          setState(() {
            secondButtonText = 'video saved!';
          });
        });
      }
    });
  }

  // ignore: unused_element
  void _saveNetworkVideo() async {
    String path =
        'https://sample-videos.com/video123/mp4/720/big_buck_bunny_720p_1mb.mp4';
    GallerySaver.saveVideo(path, albumName: albumName).then((bool success) {
      setState(() {
        print('Video is saved');
      });
    });
  }

  // ignore: unused_element
  void _saveNetworkImage() async {
    String path =
        'https://image.shutterstock.com/image-photo/montreal-canada-july-11-2019-600w-1450023539.jpg';
    GallerySaver.saveImage(path, albumName: albumName).then((bool success) {
      setState(() {
        print('Image is saved');
      });
    });
  }
}