I would suggest a clickable prototype rather than video. You can then easily screen record a walkthrough of the app to a video but it's so much more compelling and convincing to put your phone in someone's hands and let them click.

FluidUi is a great rapid prototyping tool that is very easy-to-use and is pretty much drag & drop to make interactive (clickable) prototypes.

I've used it to demo to customers for feedback and raise funding.

There is also HotGloo and Proto.io (neither of which I've used).