That would be really cool. I think the areas that make the most sense quickly to people are zero-click info and privacy. In fact, I think maybe only one should be tackled (per video), in which case I'd pick the zero-click info.
Something like (this needs to be re-worked of course and is literally off of the top of my head):
**Duck on a white or red background**
Hi, I'm <name of duck> from Duck Duck Go.
**homepage fades in**
Duck Duck Go is a search engine, like Google.
**search starts being conducted with good 0-click**
You should use it instead of Google because you get the information you want faster.
** highlight box**
You see that red box at the top? That's the zero-click info box, which gives you useful information about your search with 0-clicks.
** other searches with good 0-click**
Often times, you don't have to even click on any links. And that's just the beginning. DuckDuckGo also has more privacy, less spam, and tons of other goodies.