As hoped (expected?), Apple (finally) released a way for developers to integrate with Siri:
SiriKit enables your iOS 10 apps to work with Siri, so users can get things done with your content and services using just their voice.
Unfortunately, only specific app domains are supported: Messaging, VoIP Calling, Payments, Ride Booking, Photo Search, and Workouts. Seems like a pretty big oversight to not have a todo/list domain, which means that I'm not going to be able to add a Siri integration for Kitchen Sync just yet.