In my opinion... this is no different than any other big company having cheaper prices. This is what Capitalism is all about.
Local retail has just as many advantages over online commerce, and if you think the people who are wielding these "find me the lowest cost" apps are going to be lost, shame on the store owners. They were NEVER your customers to begin with. People who shop based on price only are ALWAYS going to shop on price only, whether they do it inside your store, or in front of their own computer.
Big box retailers need to realize their competitive advantage is in their sales staff and in their local presence (bring it home today). If an Amazon app that speaks about saving a few dollars is hurting business, its time to retrain your store staff and teach them WHY you are different than Amazon!
For the edge cases, think outside the box and put in a sales terminal, setup an Amazon affiliate ID, and if the price shoppers come in, ENCOURAGE them to order while standing inside your store, on your affiliate terminal. At least then you can make a few bucks.