Well, now what kinds of flute support are available to help you out? There's basically three types: the stick-on kind, the clip-on kind, and the ring kind. Now let's take a look at each type and see how they work.
Stick-on flute supports are really simple! They're just little rubber cushions with adhesive backs that stick on the flute between the keys to give your left hand index finger and right hand thumb a better grip. This is quite a decent idea, and definitely the right price. (There's a couple of different brands and they come in sets of two for less than $5, available from flute stores like Flute World.) They don't damage the flute, because they don't leave any glue behind when you remove them and they are soft so no scratching.
Problems? Well, they have to be taken off to clean the flute and then they don't stick back on again so well. So they don't last too long (unless you don't clean your flute often!). And they don't really make the flute totally stable. They just give you a non-slippery surface to hold so the flute has less chance to slip.
This type of flute support is made of plastic and clips on to the flute between the keys. It also comes off pretty easily when you want to clean your flute. You have to buy one for your thumb and one for your finger separately (they're different shapes of course, and there's even two different finger styles!).
There's a couple of different brands in these too. The cheaper ones are less than $10 each, available from various places including Amazon. The problem with these is that they have a tendency to scratch the flute when you attach them or take them off (and they can break). Also, they don't fit every style of flute (they're a bit big and can get in the way of the keys) and may slip a bit while you're playing. And if you have a really expensive flute there's the possibility that it will reduce the tone quality.
Another version is a little more expensive but more substantial and has soft plastic on the inside to better protect the flute while remaining firmly attached while you're playing. This is the "Thumbport" which is clipped on to the flute to support the right thumb, and it's endorsed by a bunch of reputable flutists and flute teachers. It is available from Flute World for around $20. For more information you can check out the Thumbport website.
And, they've now developed a "Fingerport" or "Pinkieport" to support the left hand pinkie finger to add more stability in holding the flute. The problem with this one is that it only works with inline G flutes, and still may need some modification to fit around the keys. Anyway, if it fits your flute and you want to spend another $20 it might be useful!
The ring flute support is a totally different concept from the other two kinds - you wear it on your finger instead of attaching it to your flute.
Called a "Cobra" because it kind of looks like a cobra snake with its head rearing up, the ring goes on your left index finger and the flute sits on top of it. Once you get used to wearing the ring (just like wearing any ring) and adjust the angle of the tail it makes the flute really secure.
The Cobra ring is made of metal, soft enough to adjust to the size of your finger, and covered in rubber coating so it won't scratch the flute. It's available in several styles and sizes, priced around $50-$60. More information and online ordering is available on the Mistic Media website.
This style solves the problems of having to remove the stuck-on or clipped-on supports in order to clean the flute, doesn't scratch your flute, doesn't affect the tone like the larger clip-ons can, and can be used with any style of flute. Disadvantages? Well, at $50 it costs more than the others! But actually you only need one so the difference isn't so great really.
If you want to just try something that will help keep your flute stable but don't want to spend a lot of money, try the stick-on type. For less than $5 give them a chance - not much to lose there!
For the serious flute player, ready to invest (both money and effort) in an accessory that will do a great job, get a Cobra ring from Mistic Media. If you take the time to adjust it to your finger it will really hold your flute well no matter which style of flute you have, and it's so easy to take off (just like a ring!) .