While many people do hate Flash, it has been said that when Internet Explorer arrives on the Xbox 360, it will not support Flash but rather HTML 5.
HTML5 however is not used very widely throughout the internet and plenty still are hanging tightly to Flash. On the other hand, plenty of people probably won't want to use the web browser on their 360 (it's Internet Explorer after all). So it may turn out to be a non-issue.
Using Internet Explorer on the 360 will require either the chatpad/controller or tablet with SmartGlass technology. Internet Explorer is set to be available on the next dashboard update in the fall of this year (most likely). It may in fact come out in December, but it doesn't have a definite release date just yet.