It's been three years and ten releases since this question was posted, and still no signs of flexipages being exposed as first-class objects. I frankly don't understand what is meant by the answer which says to "use our capabilities combined with your custom components, objects, and logic to deliver a great experience that can be further customized by your subscribers." How can they customize layouts that are meant to be parts of composed pages?
The answer to the question, then, is that to accomplish this you would need to write your own component to display a flexipage, which actually might not be that horribly difficult.
Of course, you are then still left with no ability to customize, wrap, or curate the app building (page composition) experience--I mean AppBuilder exposed as a component itself-- so there's no way to personalize this for your own products purposes. Maybe in version 92.