Is there a product to auto-build indexes based on slow queries?
No, there is no product that does what you describe automatically. At least not for MySQL.

There are tools that identify slow queries, and even run EXPLAIN automatically, for example pt-query-digest. But deciding on the right indexes is up to you. There are too many exception cases where you might choose to create a different index, or avoid creating the recommended index, regardless of the advice of the tool.

You might like to read my presentation, How to Design Indexes, Really. It's not that hard to learn to do it.