Just yesterday, Microsoft detailed some changes coming to Cinemagraph's backend through OneDrive and today, that updated app is now available. Labeled as Lumia Cinemagraph Beta, the app can be downloaded through the Store though currently the link is not searchable (so you need the app's direct link, found below).
The biggest changes in this version affect how you share Cinemagraphs detailed in the Beta release notes.
Full story from the WindowsCentral blog...