How do I restore the microphone button on my Galaxy keyboard
Did you by any chance disable the Google App in your application manager? 
 To find out go to settings>application manager then swipe over past "running apps", "all apps" options until you see a list of "disabled" (or "turned off" on some devices) apps. Look to see if the Google App is deactivated. If it is, click on it and press 'turn on'. 

I disabled my Google app a while back because it was using a lot of data in the background and I never use that app.  It took me a few days to figure out why my voice input no longer worked because I don't use it that often. Apparently though,  the voice input function is routed through the Google app, so disabling it will make it unavailable.