No.
You could save the SWF file, you could write a script to launch it in a browser or swfdec or whatever, but that particular app is highly unlikely to work if it's not actually running on that website.
In fact, I just tried that, and it, in fact, does not work when loaded from your hard drive.
Try it yourself:
Code:
wget http://express.paltalk.com/Paltalk.swf
google-chrome Paltalk.swf
As to the other part of the question:
Can you package an SWF into a standalone executable so that it runs as a desktop application? No you can't.