If it's just a SWF file, and not a full AIR app, Adobe still makes the Flash Player projector content debugger available for developers to download:
https://www.adobe.com/support/flashplayer/debug_downloads.html
This is a standalone exe, and not a browser plugin, so it will still run on Windows, macOS, and Linux.
For AIR apps on Linux, you must package your app with captive runtime using HARMAN's latest SDK. There is no "shared" runtime for Linux anymore. When you package with captive runtime, it should result in some kind of executable that you can launch like any program. Be sure to check HARMAN's release notes for information about Linux.
However, if you only need to test/debug your AIR app locally in AIR's debug simulator, you may be able to run something like this in a terminal with the AIR SDK:
adl MyApp-app.xml
More complex AIR apps with assets or native extensions may require additional command line options passed to adl. Good luck!
That being said, you might also have luck creating an AS3 & MXML project in VSCode and launching the AIR app with the SWF debugger. The options passed to ADL are mostly automated in that case, so there tends to be less that you need to guess. The last time that I tried VSCode with the AS3 & MXML and SWF debugger extensions on Linux, everything worked pretty well.