well, for starters you have to choose the music you are going to play.  Marching Band stuff kills tonality, and concert band stuff wants its music very straight.  What I love more than anything is to go off somewhere by myself (good acoustics such as in an empty Church is best).  If you have access to a microphone/ headphone setup (with some artificial reverb) this is ideal because you can hear yourself LOUD.  You do NOT want to feel self conscious!  This is a time of experimenting and playing.  It will find its way back into your "normal" playing.
 
The flute is capable of incredible articulation - you can practically talk with it.  This works best I have found in the first octave.  Just play one note for as long as you can.  Play it again and again.  Listen to it.  Make it sharp & flat, loud and quiet, vibrato and straight, tighten and then relax the embouchure, move your mouth around making the chamber inside your mouth bigger and smaller/ to the front and to the back.  listen, listen, listen. be silly.  I do this as a part of my warm ups (I can hold a note so long that I love using this in performance and watching the audience go bug eyed)
 
After you have played around, start adding one and then two notes - but still keep it simple. Let the notes break to each other - feel them.  Think melancholy thoughts/ feelings and cry/wail these couple of tones (and I mean cry).  When you feel it in your heart the expression is there - and if you are expressing it then you are finding that fuller tone.  I have a song on the CD called "Alone"  which is essentially one of these sessions on steriods. (it is on the website at Here )
 
You can also discover a rhythmic space slapping keys, playing wind tones and "spitting" staccato tones and clicking your tongue.  This is not easy stuff (I have never mastered singing at the same time!)  but it adds to your command of articulation and finding the edges of tones.  A lot of people shy from the whispy tones (definitely not kosher) and so never learn to use them.  Listen to some Ian Anderson (Jethro Tull) and you will hear some great whispies! (and by the way - he cheats!  He uses a harmonizer (electronic effect) that drops the note he plays by an octave and mixes it in).
 
about instruments: the one you play is very important to tonality.  The lower the tone the better, and the lower registers are very susceptable to leaky pads, (if you have a student flute with leaky pads get it re-paded - it is worth it). If you play the piccolo a lot that may be part of your problem - you may have an overly tight embouchere. If you know someone with a good flute (like professional)r better yet an alto talk them into letting you borrow it for a while.  This will give you an idea of the sound you are looking for, and you will then get to coax it out of your student model!   doug