How to make a whiteboard/flanelboard style promotional video for a mobile app?
I don't know exactly what kind of animations you're looking for, but Adobe After Effects is very popular for animation. You can even get a free 30-day trial of the software. That being said, if you're not familiar with After Effects, there is quite a bit of a learning curve, but the good news is that there are a ton of online resources (videos/tutorials/etc.) to show you what you need to do to get great results.