For what it is worth, I would think you need to spend more time playing long notes. There are several parameters involved in getting a note to play sweetly and correctly - air pressure, support from diaphragm, air flow, relaxation of your throat, shape of hole produced by your lips, position of your lips and jaw, direction of the air flow, position of the lip plate on your lips, and alignment of the head joint with the rest of the flute are the ones which come to mind. In my experience, you need to choose a note, attempt to play it long and slow and if it doesn't sound to your satisfaction then keep experimenting with the parameters that I have listed until you find a combination that does. Then keep doing it until your muscles have all memorised the positions they need to be in so that it comes naturally.
This takes patience

. It took me a while to realise that you have to do this for each note on the flute....