Have you seen Vialogue? A product of Columbia Teacher College's EdLab, it's a pretty nifty online tool that allows you to upload a video and add an interactive discussion by adding comments, surveys or questions linked to specific points in the video.
The very core of a flipped classroom is watching tutorials at home, and somehow linking to or sending home an accompanying list of questions.
Here, you have both in one place with the added bonus of students being
able to see each other's comments. It's basically a video discussion
Vialogue allows you to use YouTube videos or upload your own. It currently doesn't play well with Vimeo, TeacherTube or other video aggregators, but they're working on that.
Here's a sample Vialogue that really gets participants talking about a poem and the nature of language. And, as you can see, they are embeddable on a classroom blog or website.
Vialogue also has a feature that allows you to group lessons. As I spend this year digitizing all of mine in one format or another, that's a great feature. Students could easily work their way through a series of lessons, and they are inherently doing more than just sitting and watching.
Finally, for film studies classes, this is a no-brainer! What a great way for students to view and analyze video clips!
As of now, there's not "an app for that." I hope they're working on it, because making this mobile would be immensely powerful.
UPDATE: I should mention they were listed on the ALA's top 25 list of best website for teaching