HTML5 offers an accessible alternative to Flash for dynamic content, but browsers still have uneven support. The site html5accessibility.com regularly tracks the accessibility status of browsers for HTML5. Currently, Firefox for Windows and Safari for Mac are the most recommended options.
HTML5 and accessibility

With the entry of HTML5, an accessible alternative to Flash is offered when it comes to generating dynamic and colorful content. But web browsers still have uneven support for HTML5, making it currently not recommended for use.
The page html5accessibility periodically updates the status of browsers in relation to HTML5, highlighting the consequences for accessibility and possible solutions.
By the way, for now, Firefox for Windows and Safari for Mac are by far the most recommended