I am trying to learn double tongue on the flute, but I am struggling to do so. I can tongue well generally, but I don't understand the back of the tongue part. What syllable or method is used to develop this skill?
Step 1 is to get your normal single tonguing as clean as possible. Make sure that the tongue is moving quickly and without any extraneous movement. Also check that your jaw isn't moving at all; it's somewhat common for people to develop a "chewing" motion. If your single tonguing has extra motion, double tonguing is going to be nearly impossible.
Step 2 is to get the same kind of clean, smooth motion with the secondary tongue (the "koo", if you will) in isolation. Practice articulating a single note and focus on making it feel just as easy. This part is frustrating because it's like starting all over again, except worse because this tonguing mechanism just doesn't work as well. You've really gotta put your ego aside and accept being terrible for a bit.
Once you have each tonguing mechanism working well in isolation, step 3 is to put them together, slowly at first if needed. The last bit of advice is to push the "koo" as far forward as possible. Sometimes people struggle because they're going "tee kah" and making this giant shift between the tip and back of their tongues. Shifting it forward and saying "tee kee" should help.
My only deviation from the above answer is to try du-gu-du-gu for the double-tonguing syllables -- single tongue syllable 'du', then the 'gu' for the double. And, yes, your single tonguing should be as clean and perfect as possible before moving on to double and, later, triple tonguing. Slow, perfect practice will develop the technique(s) properly and, in time, you'll find it natural and easy to do.
Just my experience. Professor Richard Hahn was my teacher.