See this:Bergmann, J.; Sams, A. (2012). Flip your Classroom. Reach Every Student in Every Class Every Day. U.S.A.: International Society for Technology in Education
I think Piaget's equilibration theory best describes the learning that is happening in a flipped classroom. Watch video, build schema; discuss with group members, schema gets disturb and assimilation occurs. Teacher intervenes disturbing schema again and further assimilation happens which produces learning.
You may also consider Bloom's taxonomy of learning since FC aims to develop the knowledge, skills, and attitude of the students based on a planned desired outcome, goals, and objectives. I found it interesting to compliment with Piaget's equilibrium theory.
Constructivism learning theory is suitable to Flipped classroom approach. Student either individually or in a group study materials provided by teachers or found by students , then construct the solution of the problems
Great points by everyone. The one thing I would add is that the theory also depends on more than just the learning environment, especially since flipped, blended and online learning are becoming the norm.
What is your outcome variable? If you are measuring cognitive load then you may want to use cognitive load theory. Is your DV related to motivation in a flipped learning environment? If so, self determination theory may be best.
The answer for this question actually depends on the research context. Broadly speaking, self-regulated learning can be one of the choices as students need to take learning matter into their own hands in flipped classrooms. There are many scales available for SRL and even for Online SRL.
Other theories such as student-centered learning, gamification/game-based learning, social-cultural theory, can also be utilized and understandibly, the theory chosen will alter the in and out of class practices and design.
Good luck in your research.
PS: Thank you Ferhat Karanfil for bringing this question up to my attention.
I think Lev Vygotsky theory can be applied. Since this theory emphasizes that what a child learns in collaboration today he is able to do independently tomorrow. His learning takes place under a 'MKO' (More Knowledgeable Other) that can be peer, teacher or parent. In Flipped Classroom teaching strategy, these three individuals are conspicuously needed, i.e. students need their peers in class with their teachers as a facilitator, at home, parents come to aid their wards for learning.