Remember when you were in high school and thought the flute went up to high C only? The one with five ledger lines? Of course flutists are expected to be able to play above this range on a regular basis: we find many examples of C# and D in symphonic and solo literature, and high E as well. My favorite fingering for high D is Left Hand, double thumb, Right hand F# key (RH3) and pinky....that is all. This fingering is lower in pitch than many other choices and requires firm support, but I recommend it!
Sometimes working with a metronome is not enough! Staying perfectly even between the beats, or insuring each finger change is equally spaced, is difficult to hear. Listen very carefully: even if downbeats are right with the click there can be untidy moments. Emphasize the note you are skipping over by adding a little tenuto, and slowly make that tenuto disappear as you resume playing in exact rhythm. Play 'red light/green light': play two notes and stop, add a third note, stop, add one more, etc, until you have all the notes in the beat strung together and even. Happy Practicing.