In addition to the other two responses, you have to remember that Amazon is not in the last leg of the delivery business. By last leg, I mean their logistics system covers large parts of the supply chain all the way up to the part of the chain that actually brings the product to the consumer. However, for the last leg of the supply chain, they leave it to UPS/Post Office etc.

Because of this, Amazon has few resources that make sense for partnering up w/ smaller and local regional grocery stores. These stores have independent supply chains are warehouses. This is where Amazon has expertise and advantages. If Amazon teamed up with them, then they would have to rely on the store's existing supply chain logistics and infrastructure, rather than use any of Amazon's advantages.

This means if Amazon were to actually add anything besides a website and the brand name, they would have to either 1) delve into the actual home delivery business, something they do not have any expertise in as they currently outsource it to other postal companies, or 2) they would have to undertake some sort of join venture to restructure the grocery stores supply chain (thus defeating the point of trying to take advantage of the grocery store's incumbent advantages).

Thus, unless Amazon makes a big effort to expand its business by building a warehouse to doorsteps delivery system, or undertakes rebuilding the grocer's supply chain, the only thing Amazon gets out of partnering with a grocery store is running the risk that the grocer may tarnish Amazon's name with shoddy service / products.

If anything, I think it would be smarter for Amazon to just buy a smaller local / regional grocery chain in a heterogeneous market. The ideal would be to buy a lower end grocer like a piggly wiggly in a market that also supports higher end grocers. You continue operating the Piggly Wiggle/low end grocer under the same brand name and don't even publicize the fact that Amazon owns and operates it. You then slowly switch over the logistics & infrastructure / supply chain supporting the low end Piggly Wiggly to work w/ Amazon's existing supply chain / warehouses & anything new that Amazon has to build to develop its grocery service. You then launch the Amazon Delivery service which has it's own branding but relies on the same back end/logistics that Piggly Wiggly is running on. This means that Amazon's logistics for the Piggly Wiggly brick and mortar stores are subsidizing the costs of the infrastructure for the Amazon Online Grocer while Amazon works on building up the online customer base needed to justify the cost of running an online grocer. Additionally, I assume there is a small overlap between shoppers at lower end grocer's like Piggly Wiggly (Sorry I keep picking on Piggly Wiggly), and consumers who want online grocer services. This means that Amazon won't be cannibalizing much of the brick and mortar business by pressing the online store because they will probably be different customers. Amazon could further help target different customers by opening up the Online store in zip codes that have few to no Piggly Wiggly shoppers. This means that Amazon is basically opening up a virtual grocery store in an area that would normally reject the Piggly Wiggly brand but still uses the same warehouses/supply chain to deliver the goods to the consumer.