Make sure you have the proper mouth position. To play smooth notes on a flute, you have to place your lips correctly over the mouthpiece. Place your mouth over the hole of the mouthpiece and then move the hole away from your mouth so it is underneath your lips. Your lips should be in the shape of a tight "o." This will allow you to produce the proper sound.
Put your hands in the correct position. Your right hand should be over the keys at the end of the flute, and your left hand should be over the keys near the mouthpiece. Your fingers should be over the round keys, and your thumbs should be under the flute. If you are playing an open hole flute, make sure your fingers are covering the holes on the keys. If your fingers are not completely covering the holes, you will not produce the right sound.
Understand how to control your breathing. You should not breathe too forcefully or too gently when playing the flute or else you will not produce any sound. And if you do, the notes will not sound smooth. Remember to blow moderately. As you play your scales and do exercises, remember to breathe properly.
Play scales. To play smooth notes on a flute, you should play many different scales. Scales can be played in more than one octave, making it easy for you to concentrate on the sound you are producing as well as your note transitions. First play the scales with separate notes. Then play them while slurring the notes, without taking breaths between each note. This will make the scales sound more smooth.
Play high notes and low notes. In many flute pieces, you have to transition from a higher note to a lower note. Often, this can result in a choppy sound because you need to change the tightening of your lips and the fingering. To make such transitions more smooth, practice going from a higher note to a lower note. For example, play the high A and then the low A. Do this until you can play the notes smoothly.
Practice short pieces. Scale books usually have short songs or exercises that allow you to perfect your note transitions and articulation. Play each song a few times until you can play all of the notes smoothly or without large pauses between them. For example, do not take a breath between the notes of a single measure or a series of slurred notes. This can cause the piece to sound broken up.