I’ve found tuners to be somewhat unreliable for pitch. I use Korg tuners and generally tune my flutes with them only as an aide, my ear being the ultimate authority. Tuners are meant for a tempered tuning system where the 5ths are flattened and the 4ths are sharpened. On a tuner, the flute scale will look way off, with the upper parts of the scale looking way sharp. This is normal, but shocking when people first play their instruments into a tuner! Rely upon your ear.
Check the plug placement. Should be 23-24mm from center of embouchure. Modern flutes are usually around 19mm and many make the mistake of thinking it should be the same for these. This will affect the bottom D. Also, the fingers must seal well on the holes or the bottom D will pop up to the middle D. If you play guitar a bunch, the calluses on your fingers will hamper this. I have had to adopt a grip using pads on my left hand rather than the fingertips. Similarly, if the wrappings are loose, this will sometimes contribute to this.
The embouchure should be rolled towards you just a bit, so that the far edge lines up with the middle of the top fingerhole, or maybe not just quite, per your preferences. It should be set where you get the strongest bottom D.
Test the pitch first with your ear, using D or G as a drone on your tuner. You should find that you can adjust notes to sound fine on the scale without really thinking about it.
On a tuner, the 2nd octave should look something like 20-30 cents sharp relative to the 1st. Otherwise, it sounds flat. This gets more extreme up the scale.
Using my Korgs (I have an older one and a new one), the scale for the 1st octave usually looks something like this:
D - 0 cents (the bottom D is the note to use as your reference)
E - 0 to 5. Note that this note is very easy to blow sharp
F# - 0 to 5 More if I can get it.
G - Minus 5 to 0
A - Plus 5
B - plus 5 to 10
C# - Plus 10 to 15
C natural fingered 0XX 000 - plus 5 to 10
Middle D - plus 20
Now go up the scale starting at the bottom D and blow octaves - thus blow to the middle D and then the high D. Play these so they sound in pitch to you. Then look at what these look like in a tuner. You might try 0XX 000 or 0XX00X for the high D, 0X0 XXX for the C just below it (this is the standard).
Same with all the other notes. You will see the 2nd octave stretched 20-30 cents or more depending upon how you blow. Again, how it sounds is much more important than how it looks on a tuner! Your blowing pressure, posture and how you hold the flute when going up and down the scale will also affect tuning. Many play with the fixed stare method, keeping a rigid posture. Actually, as you go up the scale the head should be raise a tiny bit which rolls the flute out, in order to punch the upper notes.
If some notes such as the C#, B and A in the first octave feel a little high to you (hearing-wise), you can try adjusting these down just a bit with a little bit of soft beeswax smeared onto the edge of the hole to effectively reduce the diameter.
Hope this helps.
Casey