I've downloaded Macromedia Flash Player several times. It says the download was
successful, but when I try to run Picture Package it says I have to install
Macromedia Flash Player. When I search my computer, it doesn't find Macromedia
Flash Player.

Why does it say the download and installation were successful, but then I
can't find it, nor can Sony Picture Package?

This is most likely going to be a problem specific to Sony's Picture Package
software.

Searching the web, I see this help link:
http://www.ppackage.com/e/index.html

My team has no way of knowing how they implement FLash Player. So I think
calling them for more information would be where you should begin to figure
this out.