"Playing microtones on a concert flute is as simple as rotating the head plate towards or away from your lips (not twisting against the body!) to decrease or increase the effective length. Increasing the distance sharpens the note, and vice versa. This requires extremely-minute precision and fine muscle memory for instant execution. You may also need to change your embouchure to avoid whisper tones.
For example, suppose you want to play a tone of 449 hertz (A4+35¢). The closest note in the 12 tone tempered scale is A4 at 440 hertz, so you would need to sharpen this note by approximately a sixth-tone, or 35 cents. You would accomplish this by rotating the head plate away from your lips. This technically increases the effective length of the flute, which physics dictates would normally flatten a note, though contrary to common sense it does the opposite.
Additionally, some flutes come with holes in the keys ("ring keys") to facilitate quarter tone use. However, I do not recommend you purchase this type of flute unless if you have a desire to play in 24 EDO. These holes allegedly change the tone-color, which might be considered an undesirable side effect."
I strongly disagree with this.
It is true that rolling in or out redefines the pitch of the flute, but it also greatly affects tone and volume. As the player rolls-in, more of the lower lip covers the tone hole, which effectively decreases the size of the tone hole, flattening the pitch, but it severely dulls the tone and reduces the loudness and clarity. Subtle changes in pitch using this method are certainly possible, but a change of 35 cents on an A is not realizable. Rather than rolling in or rolling out, it's better to adjust the shape of the mouth or to redirect the airflow to affect small changes in intonation, but even then, alternate fingerings will need to be substituted to get consistent results.