Q: how to update flash player

Only from the Adobe site.

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

Only from System Preferences > FlashPlayer > Updates. Never from messages on internet sites, they can contain malware.

Our posts may have crossed, your advice is correct, and I'm sure you didn't intend to frighten the OP away from the link I gave. But if it had that unintended consequence, the link I gave above is perfectly safe. It will download an installer directly from Adobe. Either way, always get Flash directly from Adobe. Nowhere else.

Yes, I didn't see yours until I posted. Well, now OP has 2 ways to update their Flash Player.

What I like, and will really miss, if/when it's actually discontinued (they've been threatening to do this for a half year, by now), is the option to select the package installer for sys admins from the link I gave. I have three partitions/volumes on this Mac, all of which I can update using that single installer. Don't have to download a separate installer for each--or copy the installer separately into each volume, boot to that volume and then run it. Lets you change the install location.

I let my clones and TM do the heavy lifting.