Disclaimer: I’m a newbie to flute, but not a newbie to music. 
It’s entirely reasonable that you are “out of tune,” that’s it’s not the flute’s fault, and that you learn to hear these small discrepancies and then learn to fix them.
Tuning issues come about because a lot of Western music is based on the false “fact” that when you climb up the scale by seven octaves, and someone next to you starts at the same place and climbs up by twelve fifths, you both end up at exactly the same place. The problem is, it’s not quite true. If your friend climbs up by twelve fifths, he will actually overshoot you by a tiny amount. Western music pretends that this is “close enough,” though. This is why within one octave, we have twelve different flavors of notes counting the chromatics.
Now, in order to fit those twelve fifths into seven octaves exactly on a piano as an example (an instrument on which the circle of fifths can actually close, because it’s over seven octaves wide), what’s done is the fifths are squished by a tiny bit to crush out that overshoot. It’s as if that small discrepancy is chopped up finely and dusted over the whole keyboard. The noticeability of this fine dust becomes more and more obvious as you go lower, BTW. This is why low thirds on a piano make your teeth chatter, and yet thirds on the high end sound much nicer. The discrepancy is still there, but you get used to not listening for it at the piano (or guitar, where the notes are marked out for you with frets).
It’s still noticeable on a higher instrument like a flute or a violin though, and you can learn to hear it. It’s even more noticeable when you play with others since tuning comes into play whenever you consider the relationships between notes – this can be how two notes get along one after another, or in parallel when they are both played at the same time. And once you have multiple single-note players together, you have multiple notes that all have to gel well together. This means that each player has to fudge their notes the tiniest little bit to adjust for one another, for the keys they are playing in, and for the spread of the notes (how many octaves in the range that the band will cover). Tuning is a black art.
This can be a strange thing for people who play alone, or who play instruments with set tunings, which describes us both. (I’m a pianist and harpist, and play by myself almost entirely since I’m a bit of a hermit.) For you, you may be used to the way the guitar just gives you a certain set of notes with the frets, and if you have your fingers in the right place, then you are defined as playing in tune. The piano is the same way. You want a middle F#, you hit that key right there, and that’s the only middle F# available to you. It’s got that “discrepancy dust” on it, but that’s the only middle F# you have.
However, depending on who else you are playing with, and what key you are playing in, you may actually be able to sweeten that note by blowing the dust off of it in one direction or another. You do that on a fretless string instrument by moving your fingertip a tiny titch one way or another, and you do it on a wind instrument by noodging the note up or down a titch with your lips. (It is so easy to assume that “if my fingers are in the right place, then I’m playing the right note by definition,” but it’s actually not the case.)
It’s just not something you’re used to listening for. Either you play by yourself and don’t worry as much about it, or you play a fixed-pitch instrument, and you have just learned to accept the tuning compromises you have to make on them.
I’ve found three things very useful for me:
-
Get off of the fixed-pitch instrument for a while (guitar for you, piano for me) and just play your flute. I did this with a viola for a while and was staggered at how strongly the “dusty” notes sounded off to me when I sat at my piano. This effect went away after a while though, and now I can swap back and forth between both without problems since my ear has learned what it’s supposed to hear from one instrument versus the other.
-
Play against a drone. You can buy a shruti box app for your phone that’s very useful. These are electronic versions of a box often used in Indian classical music that will play reedy drones for you like the sound made by a concertina. Don’t play against a tuner – you don’t want to be aiming with your eyes. You want to aim with your ears, and learn to recognize what it sounds like when you play a note in just that right “sweet spot” as opposed to being a titch too high or low. Set it to drone a low D and then play D-F#-A-D’ up and back against it.
-
Record yourself. This feels a bit like sitting down in couples therapy while the therapist turns to your sig oth and says, “Okay. Now you tell me one thing he does that annoys you.” It’s painful but necessary. Play a piece, then let it sit for a bit. Go get a cup of coffee or something, and then come back in a few minutes. Sit quietly and imagine exactly how the song you played would sound in your head. Build a nice, clear image of what you think it should sound like. Then … hit play and hear what you actually sounded like. Chances are, the places where your tuning is off will jump out at you.
Basically, once you learn to hear what’s going on, you’ll start making the small corrections you need to make without realizing you’re doing it. This has been my experience with the viola, the trumpet, and with tuning my harp, and I fully expect exactly the same thing to happen with my flute.
Right now though, it’s something you aren’t used to listening for because you have a lot of experience with instruments that don’t enable fine corrections while playing, nor with playing with others. In time, you will learn to hear it, and once you hear it, you will learn to correct it. I did.
Sorry for the interminable ramble …
