Part of the simplicity in learning the contemporary Native American flute arises from the series of pitches that occur when one opens the finger holes in order. This combination of pitches, called the minor pentatonic scale, has some additional advantages. All the pitches play well together and any combination sounds fine. Also many harmonize well and none strongly clash. This makes it easy for playing duets with flutes of the same key. This scale is also emotionally neutral. Unlike other scales that sound more happy or sad, the pentatonic scales do not include those notes that other scales use to create tension, sorrow, or longing. With pentatonic scales, it is more about how you play than what you play.
With a musical ensemble, other musicians can play chords behind your flute that include additional pitches that you may not use. And those extra combination of pitches can amplify your intent, or just vary the melody to make it more interesting and sound less repetitive.
As a solo instrumentalist, you can also include an extra pitch that contrast with the other pitches in your prefered scale. Of course you have to use that extra pitch sparingly, otherwise it loses its power to contrast. The extra pitch may actually clash with some of the other notes. This can be very powerful. Some performers use these notes as the place to emote strongly.
You can also add extra pitches just to have more to play with. And it is not necessary to use them sparingly. More pitches can lead to more possible combinations of notes and more melodies.
So this tip is about going beyond the minor pentatonic scale. Explore those other notes. FluteTree includes an extensive set of musical scales for the Native American Flute. Try them out. Listen to how they make you feel or what cultures they remind you. Let your own ears be your guide.