Hi Tony,
Welcome to the forum! I've moved your post to the Flute Making forum since it might potentially become a thread on that subject.
Airiness: There are a lot of things that can make a flute sound "airy" or "breathy". Your material can be a factor, certainly. If the inside of your bore is not clean, or if there are fragments of wood or cane interfereing with the openings of the finger holes, it can dirty the sound a bit.
In my experience the most common cause of airyness is related to the sound mechanism. By "sound mechanism" I'm referring to a collection of things: The size and shape of the true sound hole (the hole in front of the block, for those folks who don't know the term), the width and depth of the air channel beneath the block, and the relationship of the block to the sound hole (does it overhang? Does it have a chimney on the front? Is the air channel in the block or the body of the flute?)
This is where I would look for "airyness". I think about 90% of a flutes sound comes from the design of the sound mechanism and its relationship to the bore size and key of the flute. The wood you choose makes up the last 10%. Other makers might argue differently.
If you have a clean bore and the finger holes are clean, look to the sound mechanism: How deep is your air channel? More than 1/32nd of an inch? What is the ratio of the bore size to the width and depth of the true sound hole?
If you make a flute with a 3/4" bore and you make an air channel that is 1/2" wide and 3/64ths deep, with a sound hole in proportion, you will have a loud, airy sounding flute most likely.
But that is not all. Your true sound hole is another place to look. How deep is it (front to back)? If you have a sound hole that is 3/8" wide and 3/8" deep, you will get some breathiness. Whereas if it is 3/8" wide and 9/32" deep, it will reduce that.
Also take note of how the air coming out of the channel strikes the splitting edge. Does it shoot over the top of it (having the air channel in the bottom of the block increases this phenomena a bit) or is your channel in the body of the flute, causing the air stream to strike the splitting edge head on?
All of these factors come together to make the voice of the flute, and it is almost never a single thing that gives a flutes voice a particular character. My .02 for what it is worth