The flute is one of those instruments that has a polar pattern with character. Two close miking techniques for the flute are quite common:
1. Approx. 5-10 cm away from the instrument, aiming half way the mouth piece and the left hand. Breathing can be a problem in this position so an omni such as 4006A or compact omni 4006C may be an advantage.
2. Due to its polar character the flute can also be miked behind and slightly above the head of the player, pointing at the finger holes. In fact in an overdub situation a myriad of places around the head yield very good balance.
In this case a cardioid mic such as 4011A or compact cardioid 4011C is recommended. In another overdub situation you can try miking the flute from the front with a vertical elevation at head level and about a meter away, this really reduces the mechanical sounds.
For live use, the head worn microphone 4066 is a great choice. This gives a fixed position, even when the musician moves around on stage.