For Chrome browser Flash Player comes embedded as part of the browser and all updates are pushed by Google as part of Chrome updates. For Opera, the above error you are seeing could be due to any proxy server you are directing to. Could you please go to Control Panel\All Control Panel Items--> Internet Options. Click on Connections and see which option is selected in the Local Area Network (LAN) Settings window.
Also, please provide the Adobe_ADM.log and FlashInstall.log files from the machine so that we can debug the issue at our end. To get the location of these log files please go through Where do I find the Flash Player installation log on Windows? After collecting the logs, upload/share the same and post the link of the shared files here. To see how to share logs see How to share a document .
By performing this action " Click on Connections and see which option is selected in the Local Area Network (LAN) Settings window" it shows "automatically detect settings" is selected.
If you need anything else contact to resolve the problem
Are you using anti-virus/malware/adware/etc software? If so, which one, including version?
I am not using any 3rd party antivirus/malware/adware software
Thank you for confirming.
The failure is happening due to a digital certificate mismatch. This usually happens when a web proxy tool inserts its own certificate in the HTTPS request. If you're using a web proxy tool, please disable it and try the download again. You may need to restart the browser for it to connect directly without going through the proxy set up by the web proxy server.