Adobe has abandoned the Flash Player for mobile and has no plans to go revert its decision
Google, understandably didn't provide support for Flash, or any other plugin for that matter, for now, even though the regular browser, even the one in Android 4.0 Ice Cream Sandwich does support the Flash Player, even in the new Galaxy Nexus which came out after Adobe announced that it was killing mobile Flash.
To make sure that there is no confusion or no expectations, Adobe clarified its stance and made it clear that no Flash Player is coming for Chrome for Android.
"As we announced last November, Adobe is no longer developing Flash Player for mobile browsers, and thus Chrome for Android Beta does not support Flash content. Flash Player continues to be supported within the current Android browser," Bill Howard, product manager for the Flash Platform, wrote.
He continued to explain that Adobe is still very much committed to Flash and is working on improving it, just not on mobile, at least not with a Flash Player plugin, as Flash technology is still available for mobile devices via Adobe AIR.
"At the same time, we’re actively working to move HTML5 forward via our ongoing collaboration with Google and other members of the Web community. Adobe’s proposal for CSS Regions, which allows sophisticated, magazine-like page layouts on the web, is now shipping in the Chrome browser," Howard explained.
Google has been working rather tightly with Adobe, especially with Flash, in the last year or so. Google Chrome ships with a built-in and sandboxed Flash Player on the desktop.