Couple of thoughts ... We are talking about Flute and not sax correct? I suspect some think this is sax talk. I'll put some thoughts on voicing for both sax and flute.
1. I find that voicing doesn't have as much to do with physical space (like fader was talking about) as it does with the shape of the syllable we voice. In other words, tongue placement as well as height of the soft palate. I find this true on sax and flute, although with flute you can add the extra space between your top and bottom teeth into the equation. This will affect the syllable a lot whereas it can't affect it on saxophone as much due to the fixed position.
2. Flute voicing is MUCH different as you go into the higher register than saxophone voicing is. Flute voicing gets more open the higher you go. Almost like the opposite of saxophone voicing.
3. A lot of players utilize airstream and embouchure changes to facilitate octave jumps and the changing of registers when playing the flute, but these things can be achieved, much like playing the saxophone, by just voicing and not by changing airstream and embouchure.
Have fun. Play more flute