Hi and welcome!
If you're talking abut the intrumental break, it seems to encompass a little better than two octaves, so a three octave (22 pipe) flute would be needed. However, I'm not certain that the instrument you hear is actually a pan flute. It sounds somewhat synthetic to me.
If you are planning to buy a flute and begin playing, I'd recommend at least a 22 pipe flute to start with, as the extra notes are needed to play in relative minor keys. My first flute was only 18 pipes, and I quickly ran out of notes. In my personal experience, there are two important rules: Always buy a tunable flute, and get all the pipes you possibly can. A pan flute can never have enough range. If I could afford it, I would have a 30 pipe flute.
Here is the pan flute section from the catlog of a popular supplier. It will give you a good idea of the different types, sizes, and prices of these instruments.
http://larkinam.com/category.asp?sb=&c= ... 0&x=19&y=9
P.S. My advice is only relative to the Romanian style pipe. There are hundereds of other variations, as it is an ancient instrument known to many cultures.
