The awful truth is that HTML5 video and media capabilities are a new technology and the browser war makes it even more difficult to adopt these solutions as a standard for media playback. While Flash requires the installation of a plugin, it is a reliable technology to reproduce media and stream it across multiple browsers.
While Flash support decreases on mobile devices and video and audio specifications improve, certainly there will be a future with no Flash media, but for now Flash is, at worst, a fallback solution for cross-browser compatibility.
Huge media delivery products like YouTube still rely on Flash as the primary technology. You can decide to use HTML5 as your primary technology and fall back to Flash if the video
and audio
tags are not supported or vice versa, but the choice should be made based on your application's requirements.