singing and playing
By singing and playing simultaneously, we can develop a more visceral understanding of airflow and breath support. For instance, sing a single, comfortable pitch while playing a long phrase on the flute. Do this with no interruption of sound, always observing how the airflow changes for various register shifts on the flute. When you return to playing the phrase without singing, you will discover that your legato has improved significantly and that your understanding of shifts in breath energy for the different registers makes sense. This is also a helpful exercise if you are having difficulty with your second register cracking.