what if you did some fansty work on it like salors knots in hemp that would look great and give your flute a little bump to keep er from rolling around.
Two words: Square Flute. 
What is the Eb key used for? I don’t recall any Irish tunes with an Eb. Do you play Baroque music perhaps, JemTheFlute?
I do, on a strictly amateurish self-satisfaction level, but that is neither here nor there. I regularly vent my Eb key (as discussed in various old threads and see any of the video clips I’ve posted on YouTube) in line with C19th flute makers’ expectations, and I also know some ITM tunes that use Eb as an accidental and/or I may insert it as a personal variation in some contexts - e.g. have a look at my recent Rights of Man video clip (OK, I know that isn’t the common “standard” session version of the tune, especially the B music, but it is an authentically recorded one, not my invention - but the Eb is in the A music anyway). The Tarbolton (OK, I know that is Scottish originally) as played by Michael Coleman has an Eb in the 1st bar. The Fisherman’s Lilt has one at the end of the B music. I’m sure I could think of more examples, but I certainly concede it is rare and can usually be evaded/fudged. I also readily admit I learnt classical Boehm flute initially - only 12 lessons to start and then about 5 years untutored before switching to simple system; but I have always had fully keyed SS flutes from the start of using such and as I already had the Eb finger habit, saw no point whatever in trying to lose it - it certainly doesn’t interfere in any way with ITM playing, being mostly a quite subconscious thing. All children learning Boehm flute learn to do it with no real difficulty, so I don’t know why some ITM folk have such an antipathy to it - it’s not exactly difficult and the keyed SS flutes were always meant to be played thus.
Venting the Eb key improves the intonation and especially the strength/tone of low Es on all flutes, also 2nd 8ve E on some flutes (though not all - can make it sharp on some) and is essential for various 3rd 8ve fingerings (especially E’‘’), where again some ITM can take you, especially if you say, shift a whole section of one of those fiddle tunes that go off the bottom of the flute up an 8ve. On my original R&R the low E is almost as strong as the low D when vented (if my embouchure is behaving well ).
But, as I said in my previous post, you don’t have to use it just because it’s there. I still think that, use it or not, having one is by far the most elegant solution to your rolling worry - won’t look strange at all or require any special work by your maker or adapter, and is there to use if wanted. It would be dually functional, not just an anti-roll curiosity (not that I think there’s anything wrong with those other ideas, BTW.)
Hey AZW
aren’t you glad you asked this question!? 
BenS
I am. Yes, I am.
I knew JemTheFlute would give a good answer, but that was a great one!
Sorry, I don’t believe that. Dead straight after all this time? Uh uhn. It may look so and you can’t really tell as easily with that big Eb block and key, but if we were to check it, that flute has some warpage, I’d put money on it. One of these days perhaps we’ll be at the same flute event of some sort, and we’ll put it to the test. 
Loren
Actually, this is a great idea if applied to the rings: Why not have the maker or a silver smith make up some rings with a raised pattern, could be knotwork if you’re being all “celtic” about it, or anything else for that matter - say rings with your (raised) initials around the circumference. Since it’s the rings that actually touch the table, if these were designed well, you’d have a decorative anti-roll feature that did look, well, ugly, silly or seriously out of place.
Loren
BTW, one can buy some rather cheesy looking patterned wire for ring making at Rio Grande. Not the most inspiring stuff to look at, but several of the patterns would likely do the job.
Loren
Jem
This particular part of your posting is simply not true. On some flutes venting the Eb key makes the intonation of low E worse, including at least two 19 century flutes I have, and many flutes by modern makers where the low E has been designed to play in tune when not vented.
Cheers
Graeme
Have a look at the pictures of it I’ve posted on the lichen thread, Loren. May not be engineering straight, but by eye… Not bad, huh?
Thanks to everyone for the ideas! I’ll try out the beaded hair elastic and leather thong ideas. They’re not the most elegant, but I like that they’re easily reversible.
Hmm. On second thought, the thong idea could lead to too much daydreaming.
ya know…I just didn’t see you as a reversible thong kinda guy…the things ya learn here, eh?
Sure, why not? If you turn it inside out you get double the wear and half the laundry!
Until he got a keyed flute, one local fellow had a little rubber toy in the image of a gorilla, the sort that you could hang off of a drinking glass, that he’d have grip his flute when he wasn’t playing it. Worked a treat, was great for conversation, and we called it “The Flute Monkey”.
I’d be interested in seeing an image of a Flute Monkey. That could be just the thing.
Dunno where he got it; Googling is giving me no images or ideas, either. But I swear it’s true.
Not at all the same thing I was talking about, but it could do, couldn’t it.
No, the one in question looked “real”, and didn’t have wires in the limbs; it was just shaped a certain way that allowed it to grip the flute.
Love it