On a PC, running chrome 25 (non beta) shows me a microphone icon, clicking on it prompts for input. When I stop talking, my alert call is executed. All good. On a Galaxy No
CanIUse says this functionality is available in Chrome 55 released December 7th 2016
As of M25 and M26 Beta it is not implemented in Chrome for Android.
You should star this bug https://code.google.com/p/chromium/issues/detail?id=112934
Also of interest is the continuous speech input API, so follow this issue https://code.google.com/p/chromium/issues/detail?id=116954