There's nowhere in your code where you actually try to write the PDF output to the response stream. The code that you have here writes the file to the FileStream, which represents the file storage. You can write as many files as you like in there, but without actually picking one and streaming it to the response stream, you aren't going to see the file being downloaded.
When you write to the response stream, you should really remember to set the ContentType. Here's a sample of what you need to do:
private void WriteToResponseStream(string fileName)
{
Response.ContentType = "Application/pdf";
Response.WriteFile(MapPath(fileName));
Response.End();
}