As a flute player... I have a few minor problems with how you are holding the flute. Some can be corrected if you take a look at an Open Holed flute. (I've uploaded a Still Life vector.) There are levers over the keys that a flute player does not touch while playing.
Right hand: your index finger is where the middle finger needs to go. It is between 2 trill keys, (but should only use the right most key).
Left hand. Thumb is way too far. Moving it to the being under the index finger