It would be a great fit given that the main challenge is logistics which Amazon is already a leader in. With Amazon Fresh they even have the ability to pick up the previous week's boxes and cold packs (along with delivering the rest of your groceries at the same time!). Blue Apron spends a fortune acquiring new customers, possibly up to $460 per sign up as of recently [1]. I bet the percentage of Blue Apron subscribe…
Their advantage would of course be their world class distribution/fulfillment tech, but also the fact that the costs of the food parts are mostly sunk already into the Whole Foods biz.