Well google docs now has voice dictation if that is what you are after. Details here you would still have to copy/paste into other apps if you need the text there.
as far as using a "mic" button in any text field on the pc it is not possible afaik, you might be able to use the web speech api to make a web app that interacts with an external program, but it would be a very funky workaround and a bit of code. also if it was made and shared the api key would likely be pulled by google for abuse.