Hi kevin,
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)[
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Beginning with Amazon S3[
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uploading an image with aws sdk for net[
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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.