You’ll hear different approaches to variations.
The thing I hear the most is players who seem to pick out certain phrases in a tune (or even a single phrase) as lending themselves to variations, and let other phrases stay more or less the same.
I’ve heard Liam O Flynn (to name just one) do a thing where he lays out the tune, say two times through, with little in the way of variation, to let “the tune” sink in. Then on the third time through he’ll put in a variation, not subtle, but served up on a platter for the listener. (In “classical” music it’s been said that great music balances the familiar with the unexpected.)
Then there are players who throw in variations constantly, everywhere through the tune equally. To my ear this prevents the listener from getting a gestalt of what “the tune” is. (Is a variation a variation if there’s no “tune” to vary from?)
Flute is a special case because so much of it is dictated by where you choose to put breathing-spots.
There are flute-players who tend to take breaths in the same spot every time the phrase comes around, so the breathing-spot becomes part of their setting of the tune, one could say.
Then there are fluters who vary where they breathe spontaneously, so in the three times of playing through a tune a fluter might take breaths at different spots every time.
Creating idiomatic-sounding breath-spots can require a bit of restructuring of the tune, therefore creating melodic variations. So for a fluter melodic variation is a necessary byproduct of taking breaths, unless you breathe at the same spot every time.
There are variations which are melodic in nature, and others that mainly involve changing ornamentation, though this often also impacts the melody a bit.
When I first learn a tune I’m generally getting a single version under my fingers. The first thing that happens, if the source isn’t a fluter, is that the un-flute-like bits, phrases that don’t fall under a fluter’s fingers, get changed to phrases that do.
Then I’ll start exploring breathing-spots. It’s good to have a quiver full of alternate breathing-spots. As the tune “becomes your own” you’ll be able to spontaneously breathe whenever you need to without giving it any thought.