Do you have a reference for this? Not that I have a reference to the contrary, but I'm not getting this impression at all based on the increasing number of sites that I see supporting HTML5 (more and more sites work on iOS devices).
At one point, most multimedia sites wouldn't work on iOS devices. Now, I only run into these occasionally, and it seems to be less and less frequently that I do.
EDIT: Actually, according to this[1], the Flash market is indeed shrinking. Assuming this is accurate, of course.