Chrome versions 45 and newer will find that plugins using the NPAPI architecture i.e. Java are disabled. There is no workaround for Java on Chrome and users are referred to https://www.java.com/en/download/faq/chrome.xml for using Java Web Start. Flash in Chrome is built in but on a Ask First basis unless forced to run in labs.
Safari versions 12.0 and newer will find that plugins sing the NPAPI architecture i.e. Java and Flash are either removed outright in the case of Java or in a limited availability state in the case of Flash. Users of Flash will be asked to run the plugin first. In the case of Java please see the above link to use Java Web Start
Internet Explorer versions 9-11 will still run Java and Flash plugins as the browser is no longer being developed beyond severe security updates. Those using Internet Explorer will not be provided any support due to the increased security risk and lack of proper HTML5 support.
Edge (browser not the financial software) For those on Windows 10, Edge only supports Flash and in a limited manner i.e. it will not autorun and users must give permission.
Flash support from the technology department will be available as long as the plugin itself is still supported by Adobe, Apple, Microsoft, and Google. Once support is dropped entirely by Adobe in 2019 we will not support it and will instead refer users to other content.