condenser mics do better than dynamic mics for woodwinds and flute
my choice of mic is "Shure SM81-LC Cardioid Condenser " but any good condenser mic will do
My flute is silver with gold head joint (Powell handmade professional series) and provides a very full tone but airy at the same time so placing the condenser above the tone holes usually gets the sound I like, but they can be miced behind the flute for more ambient tone and at the head joint for overblown jazzy sound.
For recording room, hardwood floors with tall vaulted ceilings work best. Room treatment can be fairly basic
Here is a vid for ya, (condenser mic in front of the tone holes, closer to the head joint)