How to save a file to Google Drive from Flutter web without a local file on disk?

I know your question is about flutter. I am not a flutter dev. After discussing this with you in comments it sounds like you are looking to find out if its even possible.

I went a head and tested this with C# and i can tell you that it is possible. All you have to do is turn your text into a memory stream and then upload that instead of a file stream. As it sounds like you already have the text in a memory stream you should be able to just upload it.

using System;
using System.Collections.Generic;
using System.IO;
using System.Text;
using System.Threading;
using System.Threading.Tasks;
using Google.Apis.Auth.OAuth2;
using Google.Apis.Drive.v3;
using Google.Apis.Drive.v3.Data;
using Google.Apis.Services;
using Google.Apis.Upload;

namespace ConsoleApp1
{
    class Program
    {
        static readonly string CredentialsFile = "ServiceAccountCreds.json";
        private static readonly string FileName = "UploadFileString.txt";

        static async Task Main(string[] args)
        {
            Console.WriteLine("Hello World!");


            var serviceAccountCredentials = GoogleCredential.FromFile(CredentialsFile)
                .CreateScoped(DriveService.ScopeConstants.Drive);

            var service = new DriveService(new BaseClientService.Initializer()
            {
                HttpClientInitializer = serviceAccountCredentials,
                ApplicationName = "Discovery Authentication Sample",
            });

            var uploadString = "Test";
            
            // Upload file Metadata
            var fileMetadata = new Google.Apis.Drive.v3.Data.File()
            {
                Name = FileName,
                Parents = new List<string>() {"1R_QjyKyvET838G6loFSRu27C-3ASMJJa"}
            };

            // Convert raw text to memory stream for upload.
            var fsSource = new MemoryStream(Encoding.UTF8.GetBytes(uploadString ?? ""));

            string uploadedFileId;
            
            // // Create a new file on Google Drive
            // await using (var fsSource = new FileStream(FileName, FileMode.Open, FileAccess.Read))
            // await using (var fsSource = new FileStream(FileName, FileMode.Open, FileAccess.Read))
            // {
                // Create a new file, with metadata and stream.
                var request = service.Files.Create(fileMetadata, fsSource, "text/plain");
                request.Fields = "*";
                var results = await request.UploadAsync(CancellationToken.None);

                if (results.Status == UploadStatus.Failed)
                {
                    Console.WriteLine($"Error uploading file: {results.Exception.Message}");
                }

                // the file id of the new file we created
                uploadedFileId = request.ResponseBody?.Id;
            //}
        }
    }
}

In theory any of the Flutter samples should work.

Use

dependencies:
  google_drive_client: ^1.0.3

import 'dart:io';

import 'package:dio/dio.dart';
import 'package:example/config.dart';
import 'package:flutter/material.dart';
import 'package:google_drive_client/google_drive_client.dart';
import 'package:path_provider/path_provider.dart';

void main() {
  runApp(App());
}

class App extends StatelessWidget {
  final GoogleDriveClient client = GoogleDriveClient(Dio(), getAccessToken: () async => Config.ACCESS_TOKEN);
  final String id = '';

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: Scaffold(
        body: ListView(
          children: [
            FlatButton(
              child: Text('list'),
              onPressed: () async {
                print(await client.list());
              },
            ),
            FlatButton(
              child: Text('create'),
              onPressed: () async {
                final File file = File((await getTemporaryDirectory()).path + '/testing2');
                file.writeAsStringSync("contents");
                var meta = GoogleDriveFileUploadMetaData(name: 'testing');
                print(await client.create(meta, file));
              },
            ),
            FlatButton(
              child: Text('delete'),
              onPressed: () async {
                await client.delete(id);
              },
            ),
            FlatButton(
              child: Text('download'),
              onPressed: () async {
                await client.download(id, 'testing');
              },
            ),
            FlatButton(
              child: Text('get'),
              onPressed: () async {
                print(await client.get(id));
              },
            ),
          ],
        ),
      ),
    );
  }
}