Flash Player is Disappearing after Downloading !

First things first, the following guide will usually get you a useful answer: 
https://forums.adobe.com/thread/1195540

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: 

• You're going to a website
• It's telling you to install Flash
• You're downloading our installer and running it
• It completes successfully
• You go back to the website
• It tells you to install Flash
• Rinse, Repeat

Most websites have some JavaScript on the page that tries to detect Flash.  In ye olden days, the page would check to see if Flash Player was installed.  If it wasn't, it was pretty safe to assume that Flash wasn't installed, so it would tell you to go download it.  In 2020, most browsers block Flash by default. JavaScript checks to see if Flash is there, and Flash doesn't respond because the browser is blocking it.  Hilarity ensues.

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: 

https://helpx.adobe.com/flash-player.html

If that doesn't help, check out that guide, and give us all the details.  We'll get you a better answer. 

Thanks!

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.