I don't think this can be done through File.Copy
The below articles are a very good examples of how files can be uploaded to AWS S3.
PHP AWS SDK (S3)
Beginning with Amazon S3
uploading an image with aws sdk for net
I know this is not the solution but you can give it a try. I see your code is in VB.Net but these links are in C#. Just a Heads up.
UPDATE: Just found another link for simple File upload Example. Check the third one.