No, Amazon has no refund policy (even though it did give refunds from time to time in the past). They will work diligently to resolve any package delays, but you won’t get a refund if they happen.
Also, you should note that the free one-day and two-day shipping available to Amazon Prime members only apply to how long the item will take to reach you once it ships. As Amazon states on their website, “Selecting One-Day or Two-Day shipping will reduce the transit time to one or two business days after we’ve shipped your order, but it won’t impact how long it takes us to obtain the item or prepare it for shipment. The shipping method time starts when the item ships.”
Therefore, it can sometimes take longer than one or two days to receive such a Prime order, as factors beyond Amazon’s control can add to the time it takes to prepare the item for shipment.