How can I keep playing online-only Flash games after the Flash shutdown in 2020?

Disclaimer: This suggestion is dangerous and can leave you vulnerable to security exploits.

You can download an old version of Firefox which does not have the Flash killswitch from https://ftp.mozilla.org/pub/firefox/releases/

You can download an old Flash version which does not have the killswitch from https://adobe_flash_player.en.downloadastro.com/old_versions/

Avoid installing the KB4577586 update on your machine. According to https://www.bleepingcomputer.com/news/microsoft/microsoft-releases-update-to-remove-adobe-flash-from-windows/ the update is optional and only available via the Microsoft Catalog so I'm not sure if that means Windows will not automatically apply it.

Preferably, you would do this all in a virtual machine dedicated to running Farmville 2.

In the end this will probably be fruitless as Zynga themselves will likely remove the Flash version of Farmville 2 from the Internet.

Although you may not be able to, it's possible the websites themselves will be able to, using the Rust language project called Ruffle, a Flash Emulator. You described it as a local-emulator, but that's not all it is.

Ruffle is a Flash Player emulator written in Rust. Ruffle runs natively on all modern operating systems as a standalone application, and on all modern browsers through the use of WebAssembly. Leveraging the safety of the modern browser sandbox and the memory safety guarantees of Rust, we can confidently avoid all the security pitfalls that Flash had a reputation for. Ruffle puts Flash back on the web, where it belongs - including iOS and Android!

Designed to be easy to use and install, users or website owners may install the web version of Ruffle and existing flash content will "just work", with no extra configuration required. Ruffle will detect all existing Flash content on a website and automatically "polyfill" it into a Ruffle player, allowing seamless and transparent upgrading of websites that still rely on Flash content.

Originally I only thought this was worth a comment. But looking at it again - if major sites like Farmville are Flash-only, it seems like they'd have a major incentive to keep their sites running. So that's one way you could keep playing online-only games, if they switch over to Ruffle.

What I didn't know, however, is that apparently Adobe will flip a killswitch and disable Flash entirely, regardless of your browser version.

This will most likely work, as long as the browser version is old enough not to have the killswitch-enabled version of the Flash plugin, so anything prior to ~2018 should work. We won't know for sure until the EOL date comes along, but it shouldn't take too long to figure out which is the latest version without a killswitch. I would also expect Flash enthusiasts to come out with patches to the latest Flash client that would block the killswitch functionality entirely.

So install a version of Chrome from 2017, ensure to completely disable its auto-update functionality and then check back on January 13th 2021 to see if you need to download a special patch or use a different workaround to force Flash to run on your machine permanently.

Note that officially speaking Flash is being deprecated for security reasons, so its better to run it inside a virtual machine to be safe - or use it on an air-gapped computer with no Internet access.

You can find old versions of Firefox bundled with old versions of Flash Player.

Firefox is open source and this kind of redistribution is completely legal. As for Flash, this might be illegal or it might be gray area (illegal but tolerated) as happens with most abandonware, or even legal (fair use for research?). Laws are different in different jurisdictions though. If legal security is required: hire a lawyer. Don't expect anybody here to know the full answer to the legal point.

You should take all the comments in all the answers here about how unsafe Flash is to heart.

I found a Firefox + Flash pack that works on a forum-based torrent site. For security, I am only using it within Sandboxie.

Depending on how much your stepfather wants to keep playing FarmVille 2 and if you can't get it running with the launcher, there is one way that might still allow Flash to function, although I'm not 100% sure and it depends on how the kill switch is triggered.

This blog from September 2020 says that the removal of Flash from Windows machines will happen via a Windows update: https://blogs.windows.com/msedgedev/2020/09/04/update-adobe-flash-end-support/

all the APIs, group polices and user interfaces that specifically govern the behavior of Adobe Flash Player will be removed from Microsoft Edge (legacy) and Internet Explorer 11 via the latest “Cumulative Update” on Windows 10 platforms and via “Cumulative Update for Internet Explorer 11” or “Monthly Rollup” on Windows 8.1, Windows Server 2012 and Windows Embedded 8 Standard. Also, the “Update for Removal of Adobe Flash Player” will be included as part of the “Cumulative Update” and “Monthly Rollup” this point forward.

If you can get hold of an old Windows 7 machine, either an old laptop or re-imaging and existing one with an old install of Windows 7, might.... might allow Flash to continue working through Internet Explorer 11 as there don't appear to be any plans to roll out the removal tool to old Windows 7 machines.

I have an old Windows 7 machine that I use for development purposes and Adobe Flash has been throwing up messages asking me to uninstall it prior to the 31st Dec 2020 deadline. This prompt may eventually force the uninstallation for Flash after the 2020 deadline, so you might need to find a way of preventing this.

Overall though, your best bet is to continue to work on getting the official launcher working.