After you have worked on getting a sound out of your headjoint, you will need to work on making that sound with ease. Once my student has been able to get a sound out of the headjoint I challenge them with being able to make high sounds and low sounds.
Once they are comfortable with this, I have them put the entire flute together.
Knowing how to hold the flute and where your fingers go is next.
Once you are comfortable with holding the flute, I recommend you buy a flute fingering chart as a guide to my next lesson. There are at least 37 different notes on the flute and your embouchure will be changing slightly with each note. This is why I start my students off with overtone exercises. A lot of teachers start a student off with one note at a time, but I feel like this creates stronger notes and weaker notes in the long run. I have heard flutists refer to the middle octave as the “easy” octave and the third octave the “hard” octave and they would avoid that octave. The way I teach, I like for them to think of every note as equally easy or difficult. I do the same when teaching major and minor scales I teach the patterns of a major scale then cover all 12 majors then start them on all the modes. The 6th mode is the natural minor scale and so this is how I introduce minor, but all of this I will go into more detail in another blog. The overtone exercises I like to use is on pg. 15 in the book “Tone Development through Extended Technique” by Robert Dick. This is a very challenging book but I find some of the exercises in his book are great for starting a student off on the right foot for producing a beautiful sound. There might be only a few pages I use for their first few years but the book is full of challenges that will prove valuable even to a professional flutist.