I've got a Gemeinhardt flute that has a beautiful tone, but no matter what I do it always plays flat, to the point where it is very difficult for me to play in tune with my symphony, a piano, etc. I am looking at buying a nicer flute, and I'm wondering if different brands tune their flutes differently? Or is this issue just with this flute (or...me)?
This is a problem I have also had with the Gemeinhardt flutes in general. My first flute was a Gemeinhardt student that I always had to play with the headjoint pushed all the way in to bring it up to pitch. Some flutes do have these intonation problems, which is why it is important to extensively play a flute in front of a tuner before you buy it. Unless you're playing on a period instrument of some sort (baroque flutes will be tuned differently because in the baroque period the tuning standard was different), all flutes from all brands should be tuned to A=440.
Also, to add. most Gemeinhardts are designed that they will generally play in tune to an A=440 scale.
The issue could be in the way that yo are playing your Gemeinhardt..... Or that you aren't playing with the correct head joint.
It is very possible for a knowledgeable player to play any note on a stock Gemeinhardt with it so flat or so sharp (more than 50 cents flat or sharp) that an electronic tuner would begin to register it as the next half step in the chromatic scale.
Buying a new flute depends much on your budget. If you're willing to spend $4000, get the Muramatsu EX. I had it as my third flute, and most of my tuning issues were greatly ameliorated. I had a student Yamaha and a Sonare with a Powell head. The Sonare with the Powell head cost about $2100, and was well worth the price. If you get a new flute and still find intonation problems, you might consider changing your embouchure or rolling out, though I wouldn't recommend the latter because it seems to take away some depth from one's tone, from my experience.