Inspired by the feature in Hey where you can read your emails as a feed, I thought about how it would be possible to build this myself with off the shelf components.
One of the possibilities is to do this with Gmail and Zapier. With Zapier you can create a feed from every incoming email with a label. You could use the Promotions category. When you use the link to the email as the link of the item you can adjust the automatic filtering when it was wrong.
Another possibility would be using Ekster with an external service that receives emails, filters and forwards these to the micropub endpoint. You could gather all promotional emails that way in your microsub server and read them with your reader.