Sorry, this entry is kind of technical.
I don't like to read the exercises written by other people, so I make up my own or play scale and arpeggio patterns that I have memorized.
One of the exercises I made up is based on a run that appears in flute duets based on the Magic Flute, which Mozart himself wrote. In the duet, the run starts on an F in the middle register, goes down to a C, goes back up to the C an octave above that, comes down to G, moves up to A, and goes back down to E and then up to F. It then repeats that movement and after that it goes up in the major scale to high F. Taking that pattern, I start on low E on the flute and play through the pattern in the key of E. Then I move up chromatically, playing the pattern in key after key. To vary things I articulate the runs in different ways.
Another exercise helps me master the modes. I start on C and play the Lydian mode (sharp F). I then add flats in the order of the circle of fifths, each time playing a mode of C: F natural (Ionian) - Bb (Mixolydian) - Eb (Dorian) - Ab (Aeolian)- Db (Phrygian) - Gb (Locrian). As I lower the notes of the scale, I go through all the modes and notice how they are related to each other. After playing the Locrian mode, I lower the C to a B and I'm in the B Lydian mode. So on until I get back to C. Playing this exercise keeps me thinking. It gets tricky when you start in a mode with a lot of sharps or flats.
Another thing I often do is play a melody that I know pretty well, like "Pennies from Heaven," and play it in all 12 keys.
These exercises haven't turned me into a great musician, but they help my musical cognition while they make me move my fingers. It's a little like saying the same thing in different languages.
