Users interested in Flash for vita generally download:
Adobe Flash Player Standalone is a free program that can be downloaded and run on your PC. It has been designed to play all Flash format files, including ShockWave Flash (.swf) and Flash Video (.flv). You shouldn't confuse it with the Adobe Flash Player Plugins for IE and non IE browsers.
Sony has provided a free solution to PSP download management with their PSP Media Manager software for PC. PSP Media Manager keeps your PSP download content (and any other files you want accessible to your PSP) neatly organized, and makes downloading from the PlayStation Store relatively simple. Don't look for a Mac version, though--there isn't one and it doesn't look like there ever will...
Additional suggestions for Flash for vita by our robot: