You can't open-source marketing and the insane delivery network Amazon has. Those, among other things, are the reason they are successful. They could release all of their software completely open source and literally nothing would change.
What you want here is an open source replacement for Amazon's product search that will find products from multiple independent sellers. The hard part is probably how to curate it; you want to allow legitimate small sellers without allowing the thing to be filled with scams. But Amazon hasn't done a very good job here either, so maybe it's not a high bar.
And then a payments system which is something in the nature of GNU Taler.
Amazon's logistics is an advantage, but is it an advantage that can overcome the need to pay them a vig instead of having the product shipped directly from the manufacturer? Lots of people willing to wait a week for shipping if the price is 10% lower.