This sort of thing has been done before (with gif) using imagemagick. APNG is not an official file format - the PNG group doesn't support this extension. Even if you get this to work, you are likely going to have lingering issues. You should probably consider an animated gif, unless you have some reason you are forced to use png.
Checkout the page on Video Handling. Also take a look at Animation Basics and Optimization.
I appear to be able to convert avi to apng directly on linux, but it fails on windows. A work around on windows would be to convert the movie to a sequence of stills:
convert test.avi frame%04d.png
if you want to use ffmpeg, this will extract frames every 5 seconds:
ffmpeg -i test.avi -y -ss 5 -an -sameq -r 1/5 frame%03d.png
then making the animation by using the apng edit firefox plugin.