This is something that I figured out a while back and incorporated into my own personal style. However I never had a very good way of explaining it. I love hearing a flute played this way, because there's a sense of energy, and the music sounds more alive. I always thought of it as playing with bounce, but that really wasn't a good way of explaining it to someone else.
Nina Perlove has this video that does a much better job. She calls it playing with "Pop."
I realize this style isn't for everyone. Many flutist like their sound to be smooth and even... but I don't... so there! Just kidding... play how you like, and love it!
FYI last time I watched this video it was really out of sync, so if this buggs you just listen and don't watch ;-)