Adobe Air error message - macOSX Catalina

I've not had a chance to try it , but maybe packaging with the AIR run time + setting AIR config to 64-bit.
Seems Catalina only runs 64-bit software.
From:
https://community.adobe.com/t5/Air/How-do-I-create-a-Captive-64-bit-Adobe-Air-Application-For/td-p/9828809

Step 1

Make sure you have downloaded the correct SDK and you have added it to your project

Step 2

Add "-swf-version=40" (without quotes) into the Project properties -> compiler options -> Addition compiler options

OR

Add this to your .as3proj file <option additional="-swf-version=40" /> (if you do it this way, you will have to close and then re-open your project for this value to take effect.

Step 3

Add the NEW <architecture>64</architecture> into your application.xml file. I put this just below the <name> node

If you don't add this new node into your application.xml file, it will default to a 32bit application

Step 4

Build your Air Application.

I hope this helps people out and thanks a lot to ASWC for the help

Same issue here

I am having the same problem.  I need solution to this asap.

I'm receiving this message upon updating to Catalina, as well.  We have a critical Flex application that depends on AIR to function.  Given the recent news of Adobe AIR's handoff to HARMAN I wouldn't hold my breath about Catalina support (at least, not without having to shell out big $$$).  Might be time to abandon AIR in favor of Electron...

In any case, for now it looks like you can get AIR (and any apps that depend upon it) to work by disabling System Integrity Protection on your Mac, but that's an extreme measure that I wouldn't advise outside of limited testing.  Seems like the AIR framework must try to install itself into the now read-only system partition.