Flash Player is pre-installed on Win8.1 and ships as a component of Internet Explorer. I don't believe that simply running our standard uninstaller will remove Flash Player from Internet Explorer.
As an alternative, you could install Google Chrome, which also bundles it's own distribution of Flash Player.
I believe that the original issue that you were running into is an issue introduced by Internet Explorer 11. IE11 makes it difficult for developers to differentiate between Internet Explorer and other browsers. This has the side effect of breaking a lot of code on individual websites that previously performed actions specific to Internet Explorer, like loading or detecting the presence of the ActiveX version of Flash Player that Internet Explorer requires, or correctly setting up the Flash to JavaScript communication channels that are unique to IE.
In most instances, enabling Compatibility Mode for that particular site will get things working again as expected, but the long-term solution requires everyone building sites on the web to update their code to accommodate Microsoft's new philosophy. This will be a continued source of frustration, and you'll probably want to familiarize yourself with compatibility mode in Internet Explorer, as it will probably resolve a lot of the general weirdness that you encounter when using this browser.