Windows Security Update KB4503308 for Adobe Flash Player

The update comes from Microsoft, not Adobe.  We can't diagnose their installation failures.  The best we would be able to do is perform an internet search for whatever error the Microsoft Update is returning.  They're the ones best equipped to troubleshoot their Update failures. I'm sorry they were of no help to you.

Performing Google search for problems installing KB4503308 returns numerous results for various June 2019 updates, not just this one.

A quick scan through some of them suggests running System File Check (https://support.microsoft.com/en-us/help/929833/use-the-system-file-checker-tool-to-repair-missing-or-corrupted-system​) and/or troubleshoot update failures (https://support.microsoft.com/en-us/help/10164/fix-windows-update-errors​) may help.

If you installed multiple updates on the same day, it's possible one of these is contributing to the failure of KB4503308.  You can try uninstalling all updates installed on that day and then install them individually, one by one. To view the Update history do one of the following:

• System > Update & Security > View update history > Uninstall updates
• Control Panel\All Control Panel Items\Programs and Features > View Installed updates)
  
  

These are just suggestions and Microsoft is the one best equipped to troubleshoot Microsoft Windows Update failures.