I've tried dozens of times to download the Flash Player , but after trying to get it started it disappears from the download folder. What is going on ?
The online/shim installer (that downloads Flash Player silently in the background) deletes itself after installation.
but after trying to get it started
Not sure what you mean by this. Flash Player is a browser plugin and only works in the browser to view Flash content. Unless you're attempting to view a SWF file, in which case you'll need the Flash Player projector, which is a separate download from the Flash Player browser plugin.
First things first, the following guide will usually get you a useful answer:
It would probably be helpful to step back, describe what it is that you want to do, and then what's happening.
Here's my guess:
It's pretty likely that nobody has updated <insert your favorite flash game website> since it was published back in 2007. So, the page loads, doesn't see Flash, and then gives you some vintage advice (install Flash), which also happens to be wrong in today's day and age.
In this instance, what you probably want to do is just enable Flash in your browser:
If that doesn't help, check out that guide, and give us all the details. We'll get you a better answer.