Flexible Map v1.14.0 has just been released. This release updates the Google Maps API version to 3.2, and adds a second API key setting for server side requests.
Google Cloud Platform Billing Account
Server API key
Along with the API changes Google has made, server side requests to Google Maps no longer work without an API key. Well, OK, they “work”, once per day or something, and then they get a REQUEST_DENIED error.
You can update to the latest version from your WordPress plugin admin page. Here’s the full changelog for Flexible Map.