flowering is induced by the changing of photoperiod. june 21st is the longest day of the year. after that the days get shorter, thus initiating flowering. so saying 'around' june 21st is the most accurate you can get. I tried to get more accurate and it didn't make sense.
http://en.wikipedia.org/wiki/Day_length
you'll see that it's around the 270th day of the year that 12 hours of light is prevalent in much of the northern hemisphere. That would be September 27th(Ironically). I'd say most plants visibly start flowering around late July or early August.