Sound quality and technique are only as good as the music they serve, which is why I try, both in my own music and in my teaching, to always have clear musical ideas to guide the technique of flute playing. Technical work is necessary, of course, but it is much more rewarding when done in the service of your music.
My methods are derived from the French School, and all of my students work with classic exercises by Taffanel and Gaubert, Moyse, and Reichert. I assign études and repertoire based on what I think the student would most benefit from exploring at that time. Students are highly encouraged to explore the repertoire on their own and to bring in any pieces that they want to study.
In addition to private lessons, I have experience teaching sectionals and masterclasses. I saw the benefits of group lessons while studying in France, where everybody in the studio observes each others' lessons. As a student, you get to learn from others' experiences and mistakes, which is infinitely preferable to learning from your own. As a teacher, you find yourself having to repeat things less often. I try to do group lessons when I can, either in masterclass format for private students, or in sectional format for band or orchestra flute sections.
I encourage daily practice (or as close as you can get to it) to become comfortable with your flute, which should, in an ideal world, feel like an extension of your breath. Additionally, studying the music, not just the repertoire but also the études (why did so-and-so write this exercise?) and the scales (why are scales?), will help to make music an extension of your thoughts, like speech. By learning to become comfortable with yourself, your flute, and your music, you learn to express yourself in a genuine way. Nobody will ever completely achieve this, but the journey is the divine comedy of every artist's life. My job is only to be your companion-guide, not to sit on a mountain and say that I have all the secrets; I cling firmly to the belief that I can learn from you just as much as you can learn from me.