It's a really interesting question. Most people assume it is grounded in accessibility, inclusion and differentiation. And it does hold great potential in this area, notably for gifted students. However, a fully flipped classroom (flipped all the time as is now done in some HE departments) raises accessibility issues too, especially for neuro-diverse students who may find constant interaction with peers in class just too overwhelming. As a model it ease accessibility for some but creates barriers for others. So I'd be reluctant to accept that it fits neatly in our literature on Inclusion and differentiation. Another theoretical grounding for it is simply social constructivism. I personally feel that that is the best theoretical fit: the teacher as mere facilitator, instruction that is student driven instead of being teacher led, knowledge as co-constructed, etc.
From the many articles that I have read, I couldn’t identify one theoretical framework that underpinned all or each one of these studies. Yes, some studies used constructivism. Yet, as long as students are going to use ‘tools’ or ‘instruments’ , I think that the theory of ‘instrumentation’ can also be a theoretical framework that may underpin a part of the ‘inverted classroom ‘ pedagogy. Till a clear, well defined and solid theoretical framework for this pedagogy is established, I think that a combination of theoretical frameworks, rather than one, will be necessary.
In reply to your answer, yes, if technology is involved then there is space there for activity theory or affordance theory. We need to remember though that the flipped classroom does not inherently make use of tech. Though it is at times difficult to remember, the key component is not tech use, but rather this desire to use face to face time for social constructivist activities, and to push the 'transfer' of mere content or accessing resources to outside the class. Quite a few flipped classroom advocates do this without relying on tech (particular;ly if they work in socio economic environments where they are worried about the digital divide). This makes adopting a theoretical framework even more difficult. My observations has been that researchers use diverse theoretical underpinning because their views and definitions of the flipped classroom actually varies widely.
If it is a theroretical framwork you are looking for, look wider. I think that possible theroretical frameworks for the flipped classroom phenomena and similar should have a foundation in general theories about the information society and -economy. You could formulate something just for understanding an existing practice, but it should have a context for any deeper understanding. Likewise, "e-learning" is no new learning theory in itself, and "distance learning" is, as all learning, a phenomenon as local as the learner, etc - although learning is made possible by better communication, it has no center-periphery pattern to start with. Increasingly better ICTs for documentation and communication makes people in a social process more free to variate time and place conditions in many patterns that are different from yesterday's. Check out prof Luciano Floridi's Philosophy of Information and Ethics of Information. There is a promising attempt to formulate new "prima philosophia" for human self-understanding.
If you are attending OTTAWA 2018 conference to be held in Abu Dhabi from 10-14 March 2018, I invite you to attend my Conference Workshop on Monday 12 March at 8:30 am, titled "Flipping Classroom: A Mechanism to Foster Active Learning". See attachment
Conference Paper Flipping Classroom: A Mechanism to Foster Active Learning