Flash has quite a few critics as there can be compatibility issues between browser and mobile devices. Many mobile devices do not support flash and if the website was for a business they would lose potential customers as a result of this issue.
Currently the Creative Cloud version of Flash supports enables developers to export to HTML5 however I would say that this is very much in the beta stage as Flash CC only exports the animation into HTML5 and doesn't attempt to convert the action script to HTML5. This is a real shame as I would of used Flash CC to generate a rough design of my website and then would of exported my design into HTML5 where I could then implement more complex functionality in Dreamweaver.
I am confident that Adobe will build on the HTML 5 exporter tool so that in future releases of Adobe Flash they would enable developers to convert their Action script into HTML 5.
The reason it's important to convert Flash files into HTML5 is because HTML5 doesn't have as much limitations as Flash as HTML 5 files stay consistent and can be viewed by almost every mobile device with a browser.
The introduction of adobe muse and edge animate have enabled users to modify their HTML 5 websites in various ways for example adding transitions to page elements. Currently for users of the adobe suite who want to build HTML 5 websites they are stuck with a workflow which fundamentally revolves around the use of Dreamweaver.