Assuming :
[ol]
[li]a Humanoid shape[/li][li]a height of 3 to 8 inches[/li][li]muscles with proportional strength like an insect’s[/li][li]gauzy, insect-like wings[/li][li]and Human/mammalian lungs[/li][/ol]
but excluding Pixie Dust and the Belief of Children in Fairies…
could a “pixie” fly?
Tinkerbell has arms, so isn’t using her pectoral muscles to drive the wings. So there is an issue with exactly where the drive for the wings is coming from.
Her cartoon body, with its ridiculous height to width ratio is going to have some useful weight savings. Even so, there is little chance an insect like wing would not buckle. She is a lot bigger than the biggest dragonfly.
The aerodynamics at that scale does help. When you get small the Reynolds number is smaller. Air behaves differently, and smaller wings work.
But you need to work out how Tinkerbell’s body powers the wings. They seem to be glued to her back with no power. That needs pixie dust.
I don’t have it ready to hand, but Jack L Chalker dealt with the subject in his Dancing Gods series. According to him, and in his universe, the wings are more symbolic than functional: they indicate that an individual belongs to a species which has flight capability in its nature. For example, one character has “wings” which seem to be a cross between a bat and a flying squirrel (they’re attached to her arms rather than to her back), but she can definitely fly.
Of course, that’s Chalker’s version. Barrie may have had something else in mind.
Neither magic nor bizarre or unnatural anatomy and physiology are required. Tinkerbell is (was?) actually a mutant moth emitting hallucinogenic pheromones inducing the illusion of a speaking, scantily-clad human woman.
Or she’s just a coma fantasy of one of the kids who jumped out of a window and busted open their head.
What kind of bones does she have? Human? Bird? Some kind of fleshy, skin-like exoskeleton?
Bird or similar.
She’s not that small. The difference in Re# matters for insects, but not for something her size.
Evolution has already produced lots of flying organisms in that size range (birds and bats), and they have all developed rather similar characteristics. If you want to know what it takes for something that size to fly, look to that group and see what they’re made of. The short version is that gauzy, insect-like wings aren’t going to make the grade, but if you fix that - give Tinkerbell some wings maybe like a bat, i.e. a thin membrane attached to a sturdy array of bones - then ISTM she should be able to fly.
A Google Image search for “tinkerbell” shows nonexistent flight muscles. Bats and flight-capable birds have very substantial pectoral muscles and relatively insubstantial leg muscles. Here for example is a good anatomical sketch of the musculature of a bat, and here’s a sketch of a bird’s flight musculature.
TL,DR: a flying organism the size of Tinkerbell is clearly possible, but it won’t look much like the Tinkerbell we’re familiar with.
Does this mean she has insect muscled scaled up to 3~8" size and proportionally stronger, or human muscles scaled down and proportionally weaker?
Maybe her wings are batlike. That is to say, maybe her wings aren’t entirely membranous, but have a rigid outer frame, with a thin membrane stretched across it. It’d still look about the same, in the style of images we have of her.
That’s not clear to me. Insect wings have in the past supported animals with a wingspan of 70 cm
https://en.wikipedia.org/wiki/Meganeura
So not sure about ‘gauzy’ but it seems like insect-like wings are a possibility.
I think ‘humanoid’ is the problem; you can’t get enough wing muscle anywhere on a humanoid body, whether insect or bird/mammal muscles.
On the other hand, if we leave out ‘humanoid’ and insect-like wings, and slightly relax ‘mammalian’ lungs to ‘tetrapod lungs’ we’ve got:
3-8 inches,
tetrapod,
brightly colored, green body,
wings,
flying, able to hover in place or move fairly quickly,
doesn’t eat real food, just lives off of flowers
Um, paging colibri?
As usual, Disney bowdlerised Peter Pan and turned the spiteful fairy Tinkerbell, into a ‘nice’ fantasy character. Barrie was a strange character and his earlier story about Peter Pan, The Little White Bird, is quite disturbing. A.S Byatt writes in The Guardian - * "It is a strange mixture of saccharine and soulless. Barrie’s chilling portrayal of Peter’s inhumanity almost gets out of hand - the narrator sweetly describes the little graves Peter makes in the gardens for babies who fall out of the perambulators and die, but he then insinuates that Peter may sometimes have buried them alive. “I do hope that Peter is not too ready with his spade. It is all rather sad.”*
The original illustrations show Tinker Bell as a much more child-like figure.
Flight would require stronger, so stronger.
Her size is shown very inconsistently; she’s sometimes depicted as being about the same size as a spool of thread, or small enough that from a distance she just looks like a small ball of light like a firefly. One inch might be a better estimate.
Tinkerbell has way too much mass in her hips and legs for real flight; more than half her body would be dead weight for those tiny wings to lift. Also I can’t see any kind of musculature where the wings attach… you’d have to radically redesign a human torso to be able to power wings strong enough to lift a body with our design. Even if you packed on enough muscle to power a set of wings you’d probably tear the rib cage apart from the stress.
When <i>Peter Pan</i> first opened as a play all you needed to fly was to believe. After a few weeks of kids launching themselves off of beds and bureaus it was amended to believe and a helping of fairy dust.
…
That helped until the 1960s. 
Perhaps pixie dust contains Pym Particles - because it seems like the same aerodynamics calculations would apply to the Wasp from Marvel Comics.
Eh, her wings are motorized, and presumably have a power source that’s more efficient than animal muscles.
