DrawerScreen.dart

import 'dart:async';
import 'dart:convert';

import 'package:flutter/material.dart';
import 'package:http/http.dart' as http;

class DrawerScreen extends StatefulWidget {
  @override
  _DrawerScreenState createState() => _DrawerScreenState();
}

List data;

class _DrawerScreenState extends State<DrawerScreen> {
  @override
  void initState() {
    super.initState();
  }

  Future getData() async {
    var response = await http.get(Uri.encodeFull("https://devuz.ru/api/1/catalog"), headers: {"Accept": "application/json"});
    return json.decode(utf8.decode(response.bodyBytes));
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(body: _buildNewTiles());
  }

  FutureBuilder _buildNewTiles() {
    return FutureBuilder(
      builder: (context, snapshot) {
        if (snapshot.connectionState == ConnectionState.none && snapshot.hasData == null) {
          return Container(
            child: Text('Nothing to show'),
          );
        }
        return ListView.builder(
          itemCount: snapshot.data.length,
          itemBuilder: (context, index) {
            var element = snapshot.data[index];
            return _buildTile(element);
          },
        );
      },
      future: getData(),
    );
  }

  _buildTile(element) {
    return ExpansionTile(title: Text(element['name']), children: _buildChildren(element['children']));
  }

  List<Widget> _buildChildren(List children) {
    List<Widget> childCategories = [];
    children.forEach((childCategory) {
      childCategories.add(ListTile(
        dense: true,
        title: Text("@" + childCategory["name"]),
        subtitle: Text(childCategory["name"]),
      ));
    });
    return childCategories;
  }
}

проверку на null добавь и не будет валиться до загрузки