If you wanted to continue using Flash content, you would need to either install an alternative browser that continued to run the plugin, install an add-on that emulated Flash, ask the website to emulate it, or wait for the content to be ported over.
Flash can be emulated to some extent with browser add-ons like Ruffle. Newgrounds already implements this without an add-on for much of its older Flash content. Note that it cannot currently run ActionScript 3 content, which is the stumbling block all Flash alternatives seem to run into.
https://ruffle.rs/
https://www.newgrounds.com/portal/view/59593 (example game)
If you need full compatibility with Flash, your only real option right now is to install a browser that still supports traditional plugins, like Waterfox Classic. It will continue to support NPAPI plugins after Flash is discontinued.
https://www.waterfox.net/download/