"Pre-purchase Overwatch at a selected retailer, and your retailer will give you two Open Beta early-access keys for your specific platform before the early access period begins—one key for you, and one for a friend. Distribution varies by retailer, so check with them for additional details.
If you previously pre-purchased Overwatch at a selected retailer, contact your store to find out how to receive your early-access keys."
First off, I’d check the different areas of your email, to make sure if didn’t get put somewhere like spam, or promotions.
If you still haven’t received any emails with a code, then try contacting Amazon?