The flute is among the least ergonomic of musical instruments, it is played off-centre to the body, and requires the player to maintain an unnatural rotated postion for extended periods of time. In addition, some flautists poke their head forward or tilt their head down to the right side in order to relieve strain on the right shoulder.
This prolonged rotation can overload the muscles of the neck and shoulders and create tension on the nerves in the area supplying the head, neck, arm, down to the fingers. Try to avoid prolonged practice without breaks, a 5 minutes break every 20 minutes practice will allow the muscles to relax and recover.
Exercises
Try these stretches for a few minutes following practice to help maintain nerve mobility
This article has some nice ideas on what to watch out for in playing posture and some further exercises to guard against the build up of any muscle tensions.
Accessories
The thumbport is an easy accessory to fit to your flute to help with the stability and take some pressure off your hands.
Or more radical is the vertical flute head joint which turns the flute into a symmetrical instrument similar to the clarinet.
http://flutelab.com/flutelab.com/vertical-flute-headjoint/
If you are experiencing any pain or discomfort playing the flute, or would like to find out more about preventing playing related injuries you can contact me here.
Happy Playing.