Your green branch will start losing moisture content immediately after being cut, so the ends need to be sealed as soon as possible, otherwise they will split in what is referred to as "end check".  Make sure that you also seal the knots, which are really the ends of other branches.  The opportunity to prevent knots from checking, by sealing them while still green, is another advantage to working with green wood.  When a branch has dried on her own in nature, through the elements, her knots will have more than likely checked.  When unchecked and finely finished, knots are amazing to look into, with their concentric growth rings.  Like looking into the heart of the tree herself.  Into creation itself.  Growth rings are natural mandalas, like medicine wheels, representing what Black Elk referred to as "the nations hoop"

Medicine Wheel, WyomingEverything the Power of the World does is done in a circle. The sky is round, and I have heard that the earth is round like a ball, and so are all the stars. The wind, in its greatest power, whirls. Birds make their nests in circles, for theirs is the same religion as ours. The sun comes forth and goes down again in a circle. The moon does the same, and both are round. Even the seasons form a great circle in their changing, and always come back again to where they were. The life of a man is a circle from childhood to childhood, and so it is in everything where power moves.  Our teepees were round like the nests of birds, and these were always set in a circle, the nation's hoop, a nest of many nests, where the Great Spirit meant for us to hatch our children.  ~ Black Elk

For the same reasons I like to preserve knots, I like to make intact, unsplit branch flutes.  At first, when learning to make them, I split the branch like other makers did, gouging out the air and sound chambers and gluing it back together.  But I found that method to be limited to softwoods, as it's very difficult to gouge out a dry hardwood like oak, and oak is one of my favorite trees.  And too, the glued seam running the length of the wood detracted, I thought, from the beauty and natural strength of the branch.  At each end, the hoop of the growth rings was broken.  A vision of how the dryad, or spirit of the tree might make a flute planted its seeds in my imaginationAn unsplit Birch branch flute. and in that vision the branch flute was unsplit.  Experimenting, I found that I could bore out the air and sound chambers with extended drill bits, from each end of the branch, if each end was straight enough for the respective chamber.  I've been making them this way for over 17 years now. 

There's nothing new about the concept.  Unsplit
Elderberry flutes are traditional to the native peoples of California, who made, and still make, flutes from intact Elderberry branches, poking out the soft inner pith with a stick.  I must admit here to working with a wider variety of woods besides Elderberry, as well as to my use of modern tools, like a 10 amp power drill, installer bits and wood vices.  Further details of how I bore out an unsplit branch flute are not for this article, nor am I too eager to give away so easily the hard earned knowledge of 17 years of trial and error.  There is no way to shortcut that experience, as each unique branch requires a slightly different approach--which is where experience pays off.  My intent here is to simply show the value of working with green wood in the making of branch flutes.  I do want to touch on how cutting through a hardwood like oak, with the drill bits I use (bellhanger, or installer bits) is much easier when the oak branch is green.  Green woodworkers, or "bodgers", know about the ease of working with green wood, and can split, or rive, fresh cut oak and fabricate chair parts from it using only hand tools.  Then, because of the hygroscopic properties of wood (expanding when moisture is absorbed and shrinking when moisture is lost) they can assemble a post and rung chair, without glue, through mortise-and-tenon joinery. One of the techniques these green woodworkers use, drying their rungs in a light bulb kiln, I have found to be very useful in the making of unsplit branch flutes.