No, HTML5 will not let you view Flash content. Website should update to HTML5 though as it is much more widely supported. All PC, Mac, Android, iOS, and Windows Phone browsers support HTML5. No mobile browsers support Flash going forward, and IE10 Metro for Windows 8 only supports it on certain sites.
In short, no, you will never see Flash content on your phone, but Flash content should be going away more and more rapidly from here on out.