'Application initialization error' installing Adobe Flash Player on MacOS 10.14

Thank you for the detailed information and screenshots.  It's been very helpful.

On Mac, the 'Initialization' error usually occurs when the installer APP is extracted from the DMG image.  Based on what I can see in the screenshots, it's not clear if this is the case or not.

If you did extract the installer App from the DMG, please retry without extracting it.  Just double-click the downloaded DMG file, then when the contents of the DMG file display, double-click on the installer APP

If you didn't extract the App file from the DMG, I'd like to review the installation log files saved at ~/Library/Logs/Adobe_ADMLogs.  Upload the 2 files (Adobe_ADM.log and Adobe_GDE.log) to Document Cloud (How to share a file using Adobe Document Cloud ) and post the link to the uploaded file in your reply.

With that said, it appears you're attempting to install Flash Player PPAPI plugin for Chrome.  There is no need to install Flash Player for Chrome, as Google embeds Flash Player in Chrome and all updates are released by Google.  Google does block Flash by default, forcing users to allow it for each site. When the user exits out of Chrome, the list of previously allowed sites is deleting.  If you're having difficulty allowing Flash in Chrome, see Use or fix Flash audio & video - Computer - Google Chrome Help for assistance.