Having a good, strong sound on the flute is just as important as playing in tune and having the necessary flexibility in your technique.
As saxophonists, we are used to practicing long tones and overtones. You can do exactly the same on the flute but you should do them differently. Let me explain:
I like starting out using the following exercises in overtones to condition our embouchure for the flute. I start out on the middle C and play the next 2 overtone partials upwards and then back down. I'll continue chromatically downwards until reaching G.
Upon reaching G, I will extend the exercises up to the 3rd overtone partial until reaching Eb.
Upon reaching Eb, again I'll extend it to the 4th overtone partial until reaching Db.
Finally, reaching low C, I would play up to the 5th partial.
If you are just starting out playing overtone exercises, I suggest tonguing each partial until you feel comfortable in reaching them, and then attempting to slur into and out of each partial.
I like using a method that flutist Trevor Wye presents in his books. He starts off on the middle "B" and then advances chromatically downwards toward the low C.
He then extends this to 3, 4, and 5 note groups, as well as expanding the interval.
He separates the workout into low, middle, and high ranges, encouraging the student to work on each range separately. The work is quite intense, but well worth it.
"When you play the low notes, concentrate on a point on your forehead. When playing high notes, concentrate on your feet. This will make your low notes as brillant as your high notes, and your high notes as robust as your low notes."
This is something I learned from discussions with opera singers. Thinking in opposite directions.
There are many other exercises one can do. Start off experimenting with these and expand on them.