I learned the flute along with all the other orchestral instruments when I got a bachelor's in music education, which means that I learned basic technique and how to teach it in all of them but not advanced in any of them.
The teacher had us spitting grains of rice. Is the teacher in your story eccentric? This would be a nice touch, if he is, I think.
Anyway, she talked to us about flute stuff as we spit rice (one grain at a time) all over the class. I'll bet the caretakers loved her!
When we had that down, we took out the mouthpiece only. We kept our lips in that same embouchre and blew across the hole in the mouthpiece. The bottom lip must be on the edge of the hole and then you rotate the mouthpiece until you get the best tone, or in some cases, any sound at all. When you're starting any band instrument, it's normal to start with mouthpiece practice, whether it be "crowing the reed" (winds with reeds), "buzzing the nouthpiece" (brass), or the above procedure with flute.
If you're not careful you can get very light neaded because, unlike all the other blown instruments, there is absolutely no resistance, so you breathe in and out huge amounts of air -- the paper bag thing is good if you get carried away. The teacher advised us that when we taught beginners in school, we watch carefully for faniters.
The mouthpiece thing can go on for several classes. You're trying to get them really comfortable, automatic with it before you put the instrument together. And it's not hard to keep them interested becuase this is your chance to get their whole rhythmic thing together. They play all kinds of notated rhythms, little "pieces" even, with just the mouthpiece.
Oh yes, if you blow straight across the mouthpiece you get the right sound. If you rotate it away from you, you start getting a higher not or "partial" which you don't want just yet -- it's called overblowing and gives you the higher notes. There are actually three ranges. The one you start with, then the octave above that and the next, but that takes a while.
When the student is really comfortable with the mouthpiece, you teach them how to put the instument together. It is in three pieces, the lower two with keys and the mouthpiece without. When you put the lower two together -- the lowest is the foot joint -- you hold down the keys in a certain way so that the rods (which connect the keys that you press down to the pads which are lifted off the holes in the body of the flute) are not bent. Otherwise they will eventually get bent all to hell and the repair is expensive. Then the mouthpiece is added. Always, they are put together with a twisting motion, always, for the same reason. The teacher has a fit if you try to jam them straight together because that means her repair bill, if it's a class, will go up. And from the very, very beginning, the teacher never lets the student open the case (usually with tow snaps) anywhere but lying on the floor so that the instrument does not drop.
Feel free to ask questions.