Using AWS ML to recommend products
This is a classical example of collaborative filtering, in particular you're talking about user-based collaborative filtering.

I don't think Amazon ML supports collaborative filtering (https://forums.aws.amazon.com/thread.jspa?messageID=712158), but you can do it in R and run your R code on the cloud.

It's easy in R, take a look at the recommenderlab package. The vignette has an example with the MovieLens movie rating data set. 

You may also use the Microsoft Azure ML framework as it has better support for recommender systems. Google "Azure recommender systems" will give you useful links.