Rabbit exercises, taught to me by Judith Bentley, are the quickest and most miraculous way to improve your sound. Simply put the flute up to play and open your mouth. (Ex. 1) Then puff your lips together for short bursts of sound into the flute instead of tonguing.
How can I make my mouth more flexible?
Sit or stand in front of a mirror with your face and lips relaxed. Stretch your mouth's corner to the sides without opening the lips and hold for 10 seconds. While expanding your mouth laterally, part the lips to expose the edge of your teeth and hold for 10 seconds.