In my day-to-day, I don't have any use for Adobe Air products. For work on the other hand, we have a timesheet system built by Deltech called Traffic Live. My personal views on the software or process not withstanding, there's a few steps you need to take if you're running macOS Catalina. The main issue you may encounter is that macOS thinks the Air runtime is damaged. It's part of Catalina's quarantine system.
Download Adobe Air's installer and install
Go to Terminal (apple/command + space and then search for Terminal) and run the below commands. Note, you may have to enter your password on the second step
sudo xattr -r -d com.apple.quarantine ./Adobe\ AIR.framework
The first step navigates terminal to the right folder, and the second ensures the app can install despite the Apple quarantine.
Ensure the Adobe Air application you want to run is on your local computer (e.g. in your downloads / applications folder)
That should be it..!