Flash is now discontinued for all major browsers and is no longer supported by Adobe. It is recommended that any previously used flash content is converted to a supported format ex. HTML5, SCORM 2004, SCORM 1.2, AICC, TinCan xAPI.
See the following announcement from Adobe for additional information: Adobe Flash - End of life
While Flash was once the go-to format for interactive content, incompatibilities and vulnerabilities have arisen in recent years that have raised the question: is it worthwhile to publish third-party learning content to Flash?
While Flash still remains compatible with browsers used at the desktop level, many of the most commonly used browsers are taking, or will be taking, steps to either disable or severely limit the capabilities of the Flash add-on due to the severe security issues that are discovered on a regular basis. An article found here explains some issues (Note: In the weeks after this article was published, several severe security flaws were discovered). For example, the Firefox browser recently disabled the Flash plugin completely due to security issues that were identified (though it has since been re-enabled once those issues were resolved), as well as the popular Google Chrome browser will have Flash disabled by default in their new release coming this September (2015), requiring the user to select and enable flash content on a case by case basis.
In regards to mobile devices, flash is already fairly limited in it's compatibility, specifically in that Flash is not compatible on any iOS device (iPhone, iPad etc.). While it is possible to install Flash on a Android device, it is not a stock feature on most devices.
Since HTML5 has gained more widespread adoption, it is likely that widespread compatibility will drop as Flash becomes more and more obsolete.
Several high profile and severe security issues have been discovered recently that can be used to directly compromise a users security via the Flash plugin which required several updates in the month of July alone (a quick Google search will return results that better explain some of the issues addressed).
With the potential for new issues to be discovered, the general shift away from Flash, and with widespread support for HTML5 in new and old browsers, HTML5 remains the recommended third-party publishing option of choice for the foreseeable future.
Adobe, the makers of Flash, posted a piece of news outlining their plan to stop updating and distributing the Flash Player at the end of 2020. They encourage content creators to migrate any existing Flash content to open formats. You can read more about their plans on their official blog.
All of the major browsers have also announced their plans to discontinue support of flash by the end of 2020 as well. You can read more from these organizations through their official announcements which you can reach by clicking any of the links below: