Hi Joe:
My old lathe has registration holes on the drive pulley for this purpose.
As Ed mentioned, you could also make a disc with registration holes that
are temporarily fixed to the work to accomplish the same thing if your
lathe doesn't have this feature built in.
    A purpose made rest can then be  clamped to the lathe bed then allows
for making flutes parallel to the long axis, as Ed mentions.  Rig a support
at center height from the lathe bed, and use that to mark/cut the flutes,
ensuring that the marks/cuts remain in the radial plane, parallel with the
lathe bed (at center height).  Working from the top is more difficult on
non-cylindrical objects.  You basically need to make a tool rest at center
height (center height minus ½ the width of the marking/cutting tool you are
using.  You can make it out of plywood that is cut to the profile you want
so that you have support right up to the surface of the work.  The time I
saw it done, the turner used a small trim router used on its side held in a
box, sliding it sideways on the table support, the depth of cut being
tricky if there are bumps to contend with.  You might be able to find a
video on that tube site.
    As for elliptical turning, it's not that complicated, but for large
objects you really need a very heavy, stable lathe and sandbags etc for
dampening the vibration. Even with small turnings (oval tool handles, for
example) there can be quite a bit of vibration to deal with.
Cheers from Waterloo
Claudio
snip

PROBLEM  what about the foot and the neck?  They would

> ideally be turned, but how does one turn an elliptical shape?
>
> That would work and would not take too long.  Perhaps turning it round
> first, then knocking off the high sides to bring them into shape with the
> templates

snip

>
> >
> > Anyway, once the thing is faired and smoothed and is true to the
> templates
> > it would be time to flute.  I really don't know where to start.  The
> flutes
> > would run from the foot to the neck, so they would have to get wider and
> > narrower as they rose and fell.  I guess one would carefully mark off the
> > tops and bottoms of the lines where they hit the neck and foot an let the
> > swell take care of itself.  But how does one cut straight, true lines
> across
> > something like that?
> Snip
> I have thought of this a bit for a project in mind.  I might mount it in a
> lathe and devise a way to hold it so that the flute I am working on in
> along the top - for me, it would be the right height for that sort of
> work.  I know you can buy, and therefore make, a disc that mounts on the
> piece that has some sort of register holes in it for making everthing even
> - 20 flutes, 30 flutes, whatever you decide on
>
Snip