How can I have my AppBar in a separate file in Flutter while still having the Widgets show?

This is another way of going about it. By doing this you can customize this appbar to the way you want. That way, if you continue with that style, you don’t have to recreate it on every page. You create it once and call on it within any widget.

Class

import 'package:flutter/material.dart';

class BaseAppBar extends StatelessWidget implements PreferredSizeWidget {
  final Color backgroundColor = Colors.red;
  final Text title;
  final AppBar appBar;
  final List<Widget> widgets;

  /// you can add more fields that meet your needs

  const BaseAppBar({Key key, this.title, this.appBar, this.widgets})
      : super(key: key);

  @override
  Widget build(BuildContext context) {
    return AppBar(
      title: title,
      backgroundColor: backgroundColor,
      actions: widgets,
    );
  }

  @override
  Size get preferredSize => new Size.fromHeight(appBar.preferredSize.height);
}

Implementation
within desired page

@override
  Widget build(BuildContext context) {
    return Scaffold(
        appBar: BaseAppBar(
          title: Text('title'),
          appBar: AppBar(),
          widgets: <Widget>[Icon(Icons.more_vert)],
        ),
        body: Container());
  }