Applications created with Captivate will they work after the end of Flash ?

Where it matters is your user's access to the Flash player if you have published to Flash content instead of HTML. I am using Chrome and I get regular nags now to uninstall Flash player. I know not to do that because I want to continue access to Flash assets. Most of your users will take the option to uninstall Flash Player from their browser. this means if you only published to the SWF option, they will not be able to play it. 

More than likely, though, you ran with the option to publish to both HTML and Flash if you have been using Captivate in the last five years or so when the option to publish to either or both became available. If that is the case, you will be fine when peopl uninstall Flash now. The multiscreen.html file will see thatFLash is not available and automatically load only the index.html file which is the html version. What I have done in my project with thousands of Captivate lessons is simply make a copy of the index.html and place it back into the folder with a new name of multiscreen.html. That means any location on our website or form outside of our website that happened to point to the multiscreen file will kickover to HTML seemlessly and not trigger a message from the broswer that a file is Flash and do they want to give permission to run it or get a message that Flash will be going away. It took about three days to do this for all of our thousdands of lessons, but it was worth it to be sure our students have as smooth a path to the content as possible. 

Need adobe to confirm but I am not sure thats right as it works fine on machines which are blocking SWF. 

But obviously as long as you have not used any SWF assets in the build.

Adobe clealry need to confirm this urgently