Yes sir, John! I won’t drop it! I won’t put it on the table off which it rolled either. 
Maybe trying using a more pipers’ style grip on your right hand. It’s widely used and accepted. This means keeping your RH fingers straight and bending them at the metacarpo-phalangeal joints (see illustration). Since your thumb wants to support the flute from below, let it. It should free up your pinky. I use Jean-Michel Veillon as a posture reference (see photo from Brad Hurley’s site).
Jean-Michel Veillon:
One cannot do better than to try to imitate Jean-Michel, in any aspect of flute playing! The photo Aaron posted illustrates just about a perfect example of the “standard” or “classical” or “Rockstro” flute hold. Jean-Michel is always superbly relaxed and controlled in everything he (chooses) to do - and boy, does it show! His recordings should be on everyone’s essential list. If you haven’t heard him, check him out! http://www.jmveillon.net/fr_pages/frames.php?page=fr_accueil.
I wouldn’t say there was anything of the “pipers’ grip” in Jean-Michel’s hold though - he doesn’t advance his fingers across the tube, but closes the holes with the centres of the pads, as the photo clearly shows.
Diane, I agree with the suggestion that you try varying the rotation of the embouchure/head joint in relation to the tube, and on your key-less you could also try different alignments for the upper and lower body joints, though obviously that can’t be done with your Boehm, but if you find it is rolling about, you certainly aren’t quite getting the hold right. Hand size shouldn’t really be an issue. It sounds like you are very sensibly trying to do the “right” things. They will become familiar and your confidence will grow. Pressing the Eb key isn’t wrong, and it does lend stability, but shouldn’t involve sufficient pressure to cause pain! I think you just need to give yourself enough time to form the habit of placing the R thumb - it will come with practice… as others have said/implied, many things that pose problems/seem awkward or difficult as a newbie tend to vanish from consciousness once overcome, and we only remember our own struggles with them much later when trying to advise others.
Anyone know what flute Jean-Michele is playing?
My guess is it’s a Wilkes.
Lovely photo. Thanks.
Almost certainly one of his Wilkes’s - could be either the D or the Eb. I don’t think his other flutes have as much fancy banding on them, and these days I think he only plays his Leharts in F and high Bb etc., not the “concert flute” size ones. Depends on how old the picture is, of course. It’s a while since I last saw them, but I seem to recall the Eb had more of Chris’s fancy metalwork than the D, and I think this picture may be the Eb, but I’m probably wrong…
Thanks. Well, if somebody will give me a Wilkes
I promise to be relaxed and controlled in everything
I choose to do.
If only it were as simple as that! I think it is one of the hallmarks of greatness in many walks of life to seem always as though one has time and space within what one is doing. Jean-Michel has that in spades no matter how frenetic the piece of music may be. He seems, to me at least, always to be totally in control, to have considered and to be actively considering every detail and nuance of his performance and choosing precisely what he does based on his technical and artistic mastery and his impeccable preparation. He never fails to blow me away, either on re-listening to familiar recordings or when I have the good fortune to hear him live.
Well, you’ve never heard me play the kazoo…
grateful we are too 
Since your thumb wants to support the flute from below, let it. It should free up your pinky.
I totally agree with what Aaron said.
My wrists are bent and my right thumb is under the flute. Though I still can’t play like JMV. I confess that there are times when it doesn’t feel all that secure - as when I play a C#. But I have never yet dropped it and I can play, relaxed, for hours at a time.
I spend time in the gym and on the yoga mat, which I’m sure helps enormously.
I am delighted that nobody ever told me to keep my wrists straight or to brace the flute with my little finger. Had I been a member of this forum when I started to play I might still think I was holding the flute the wrong way.
If you are always relaxed then there will be little tension and you can change the way you hold the flute in the course of a session. Generally I hold the flute a bit higher - depending on my mood – and who is to my right!
Mike Rafferty looks like you, Cocus. If anything his left wrist
is more cocked. He’s 80, I think, a great flute player.
Some people are going to do it this way and be fine,
obviously.
I used to look more like Mike R than I do now.
It was comfortable to cock my left wrist, I didn’t
even think about it, just did it. My rt wrist
was bent. Like you, I spend time in the gym
and do yoga.
I started getting a good deal of pain in my rt wrist
and more in my left wrist.
People are different,
bodies are different. Sometimes the most relaxed
and comfortable position, the one you fall into
naturally without thinking about it, leads to injury.
Not for you, obviously. But for some.
Now I am looking somewhat more like John-Michele Veillon
than like Mike R and you. Notice his left wrist,
still somewhat bent, is in a more neutral position.
The interest I expressed in my earlier post
was in a left wrist, not ramrod straight, but
in a less cocked position, a more neutral
position, like Jean’s.
The contrast in the photos of you and him
expresses different philosophies of instrument holding,
I believe. Both of you are relaxed, and his position
is more formal and more studied. I don’t think
one ends up looking like Jean by simply doing
what feels comfortable. He thought it through,
deliberately. It’s a studied position. There was
the intention of keeping the rt wrist straight,
for instance, and reducing the left wrist bend
to something closer to neutral.
There was a time when I played with a brace
on my rt wrist that kept it straight. Then I played
without the brace and attended to how it felt,
so that I managed to stop bending my rt
wrist. Then the pain went away.
Now I’m learning to hold my left wrist like
Jean’s, and the pain is going away.
No one method is going to work for all of us.
That includes the idea that relaxation is enough.
I agree that relaxation is important, but for some
of us it won’t be enough, though I appreciate
it’s enough for you and may be enough for
a number of people.
For some the relaxed
and comfortable position we begin with will
lead to pain, it may take a few years of playing,
and a more formal and studied position,
equally relaxed in the end, will be the
alternative to a lot of trouble.
Jim, don’t want to be pedantic (who, me? 
) but J-MV’s forename is, as many French (OK, I know he’s Breton really) people’s, hyphenated, which means they (almost) always use/expect to be addressed or referred to by both elements, so he is Jean-Michel (no e on the end).
I don’t do yoga or any kind of deliberate exercise, and as I only ever had a handful of classical lessons when I started, my hold and posture largely developed untutored and realtively unconsidered for many years. Latterly I have given it thought and deliberately changed (or tried to) some aspects, but I have never had any real problem with any pains or RSIs from flute playing. I have sometimes sustained RSIs from other activities - I drive for a living and have sometimes had arm or hand tendonitis or other strain, especially when a vehicle has/is developing a steering defect! - which have made fluting uncomfortable, and as I approach 50, I sometimes wonder if I have the early signs of arthritis in my hands; but caused by the flute, no. I can vaguely recall feeling insecure on open C# long ago, but not any more, and of course I usually vent the C key for this note save in swift passage as well as putting R4 on tube or Eb key depending on that’s presence, so C# isn’t “all fingers off” when sustained. C# at the break into the 3rd octave is in any case oxx xoo, so not “all open” (which is flat on most flutes).
Like Cocus (apparent in both his picture and in my signature one) I tend to droop more to the right and have to think about keeping my end up 
… J-MV usually keeps his flute very horizontal - more so than in the picture on this thread, and I agree with Cocus that it is (as I already said, like everything about J-MV) a very consciously studied and deliberately adopted posture on his part, but totally habituated and relaxed. Copy him!
Here’s another, more recent (last Feb) shot of me with my Rampone low B flute. (Wasn’t playing my R&R on a story-walk in the frost!)
One nice thing about the ergonomic placement of the finger holes is that pipers grip is not necessary. That is one thing I really like about my Casey Burns flute. My fingers go right to the holes without trying. All flutes should be this easy.
I think if I just train my right thumb to rest a tad closer to me and thus a tad less under the flute I can get some of the pressure off my pinky and yet still feel stable. I just have to train myself.
I appreciate all the information I’ve gotten here. It helped.