In ST09 it looked like Kirk was the one heading down the path to becoming a drunkard. McCoy had been going through what must have been a brutal divorce. A casual drinker doesn't usually carry a flask, but he did seem quite stressed out, too. If anything, joining Starfleet got both their lives back on track. I doubt McCoy had a flask on him on board the Enterprise.
That said, from TOS, McCoy struck me as a good southern gentleman who enjoyed a cocktail from time to time.
In earlier treatments of the TOS characters, weren't McCoy and Scotty supposed to be drinking buddies? I seem to remember that, but don't know where I read or heard it.