As stated, I like to bore out unsplit branch flutes while the wood is still green.  It's easier on the tools (as well as the muscles and joints!) and the wet, softer wood won't dull the edge as quickly, also keeping them cooler, preserving their cutting edge longer.  It also speeds up the drying process and greatly reduces surface checking of the wood.  By boring out the dense, inner heartwood, the stress between it and the less dense sapwood, as each dries at a different rate, is gone, preventing the checking caused by that stress.  I also like to leave the bark on while the branch is drying, which slows down evaporation through the outer surface.  Thus, with moisture leaving the wood from inside the bore, as that inner surface shrinks, it will pull itself together around the empty space, rather than the outer wood being pulled apart as it shrinks before the heartwood, the typical cause of surface checking. 

But boring out the air and sound chambers is as much as I'll work a branch while green.  If not dried before voicing the flute, then the nest,
Hot box with lid closed. windway, cutting edge and block may warp or even split as the branch dries and shrinks, ruining the tone.  The dimensions of the sound chamber may also shrink, affecting the tuning.  Another benefit to drying the wood is that whatever finish you use will penetrate deeper and adhere better. 

I built the light bulb kiln described and pictured on this page for about $15.00 worth of materials.  
The heat source is two 100 watt bulbs spaced evenly apart.  Their sockets have been inserted, snugly, through two holes cut into the bottom of the cardboard box, the holes lined with aluminum foil spread out around the light bulbs on the floor of the kiln to deflect the heat.  I used two old clamp lights that I had in storage, removing the aluminum shades and the clamps.  But inexpensive sockets with electrical cords can be purchased at the local hardware store.  Two sections of 2x4s were glued onto the bottom of the box to allow Hot box with lid for the light sockets and their cords.  Four dowels were cut and inserted through the middle of the width of the box, creating a drying rack for the branches.  The box itself I purchased from a local Uhaul store, their "Sport Utility Model", but any cardboard box can work, if it's long enough to hold the length of the branches.  You can see in the picture how a lid is cut into the top of the box, which makes it easy to place or remove branches from the drying rack.

This kiln
dries wood based on the principle of heat convection as well as evaporation.  No fan is necessary because of this.  You can see in the picture five holes in the lid of the box, each about 1/2" diameter.  Each end of the box also has four 1/2" holes, cut at the bottom.  With the two 100 watt light bulbs on, the air in the box heats to around 125 degrees, fluctuating between 120 and 130 depending on outside temperature.  Moisture then evaporates from the branches and leaves the box through the top five holes (with the lid closed of course), while new, drier air is drawn in from the eight bottom holes.  With the branches resting on dowels, the heat flows up and around the branches.  Aluminum foil is taped onto the inside lid of the box, helping to deflect some of the heat back down onto the tops of the branches.  The result is a fairly quick, even drying process.  Besides being inexpensive and easy to use, the cardboard box also helps to wick out the evaporated moisture.  Before placing a bored green branch into the kiln, I like to drill a 1/8" diameter starter hole where the sound hole of the flute will be.  This allows air to circulate through the long sound chamber, speeding the drying time and reducing the likelihood of any mold growing there during the drying process. 
Branch being weighed on three beam scale.
The easiest way to determine when a branch is bone dry (about 5% moisture content) is when it stops losing weight.  So I'll weigh the branch before placing it into the kiln, including a short piece of branch that will end up being the bird or block for the flute.  It's good to drill a small diameter bore through this block piece as well, that bore helping to prevent surface checking just as it will on the larger piece for the flute body.  Before weighing, I'll attach a piece of painters tape to each branch and it's smaller block piece, with an identifying number, and write that number onto a 3x5 card, one for each flute and it's bird.  For the smaller flutes I'll weigh every three days, for the larger every week, the weight and date noted on the card.  There's no need to weigh the block piece, as it can safely be assumed that when the flute body piece is dry, it's block will be as well.  Also included on the card is information about what species of tree the branch came from and where it was gathered.  Depending on size and density of the wood, bored out, unsplit branches can take anywhere from three days to one or two months to dry in the kiln.  When the branch stops losing weight, it's considered to be bone dry.  I'll then remove it from the kiln and give it a couple days to relax to equilibrium moisture content before sanding the inside surfaces of both chambers and then starting work on the voicing.  The EMC wherever the flute travels will of course vary.  But having had its wood bone dried in the kiln and stabilized through the finishing process, it should now, with care, safely withstand most livable ambient temperatures, just as it did when physically connected to the tree. 

Note: After two years of use, the cardboard box of this kiln got rather tweaked and weathered and the lid no longer closed tight enough, so I rebuilt the same design (a few inches taller) out of plywood.  In this wood version I used ceramic flange type light bulb sockets screwed to the floor of the kiln.  I've also transitioned to the use of terrarium heaters that screw into the light sockets, as their life span is much longer than a light bulb, up to 5 years.  But this cardboard light bulb kiln is a very easy, inexpensive material to get started with, while finding out if this method is going to work for you. 

8-18-10 - Added info about drilling a small diameter hole through the center of the block piece, to help prevent checking.  
8-19-10 - Added info and picture about using the light bulb kiln as a solar kiln.
12-5-10 - Added info about lining the holes for the light bulbs, as well as the floor of the kiln around the light bulbs, with aluminum foil to deflect the heat.