The standard download is a small program that connects back to Adobe for additional files. If that one isn't working, try the "full" (also known as "offline") installer from the following page:

https://www.adobe.com/products/flashplayer/distribution3.html

Find the Windows - Firefox row in the first table. You can use either the EXE or MSI package, they should both work.

Success?

Thanks for the information but I couldn't get the Flash program to install even though I have the new Firefox version.

Where does it fail? For example, you can download the file, but when you run it, you get a message? Or it seems to install correctly, but it doesn't show up in Firefox? As much detail as you can provide would be helpful to suggest next steps.