Where are digital touch messages kept? I have recently upgraded to iOS 10 and notice the new digital touch feature in Messages offers a "keep" button. Where are they kept? Can I see them in any other app, or do anything with them outside Messages? Can I export them? In what file format?
The keep option simply means they are not removed from the conversation - just as with audio messages, it's a space-saving measure.

You can long-press on a digital touch item to get a Copy option. From there you can paste it anywhere that accepts photos as paste data (such as the input field in WhatsApp or Messenger, or an image editing app that supports it). Note this will copy it as an image, and not as a GIF/video that contains the motion present in the original.