I have been working on something similar myself! You can follow the manual here to make use of the handy Video plugin: https://www.scirra.com/manual/181/video
I recommend encoding in MPEG-$'s h.264 and WebM's VP8, since VP9 does not seem to be working in my own projects, and then you can place them in your project file using the C2 project file import.
I used it for showing tutorials, and what I did was record myself playing (using GifCam) on a portion of the game screen (essentially just enough to show the mechanics), and then export in a lossless format to preserve quality for when I needed to convert it to various formats.
Or, if you have your own edited video, then you can do the exporting yourself with a video editor. If you do not have access to one that can export as a WebM in VP8, then you can use a tool such as FFMPEG through command line parameters (not sure what kind of GUI's there are available) to convert a lossless video file (such as uncompressed AVI, which you will first need to export as, if you are using a video editor such as Camtasia, or Windows Movie Maker, or Sony Vegas, & etc.).
I may make a video tutorial for this process. We shall see with what time I have available, because the Video plugin is quite a nice tool to have.