Flutecore
Respect your past, look to the future
The pentatonic scale has a couple of gaps, making it hard to play even simple melodies with it. (Something that doesn't seem to bother the Chinese. If you want some simple material to play, try searching for traditional Chinese music.) In order to play Frere Jacques, or more ambitiously, Amazing Grace, you need a few more notes. They are not very hard to find on a Native American Flute.

Let's take an A flute. The first two notes are A and C. On the piano, there are two notes in between those: the Bb and B. Can you play those on a NAF? It turns out that the B is playable with a little trick. If you rotate your hand a little, pulling back your ring finger so that it only covers half of the last hole, you get a note that is in between the A and C.

The next gap happens when you lift your left middle finger. On an A flute, you're skipping the F and F#. Is there a way to play those? Sure there is. Let's start with the F#, and we'll have a look at the F later. Are you still holding down that ring finger, just because I said so? Well, let's see what happens when you use it. Lifting your ring finger gives you an F#, so now can play a piece of a scale: E-F#-G.

Going from F# to G is a bit tricky, since you put down your ring finger, at the same time as you lift the middle finger of the same hand. Practice slowly, going both directions.

pentatonic-a-filled
So there you have it, a more or less complete scale. Next, let's see what we can do with it. (Musicologists like to put labels on everything. This is the D dorian scale. No need to remember that, as there is absolutely no point to it. Let's just go and make music.)
The ultimate guide to scales and keys: the basic full scale