Ambidexterity is usually an acquired condition; truly born cases are very rare.
For musicians, most often there is no choice than to learn on right handed instrument, as most are not reversible and left-handed ones not available (as I believe is the case with the modern traverse flute).

I mean, the difficulties for a child born left-handed would be totally excluding unless he/she learns to play on a right handed flute.

But there are several testimonies on internet from people who, being left-handed, had no difficulties to learn and play on a right handed instrument.

I'm left handed and have no difficulty playing a normal clarinet, flute and piccolo!

Maybe the flute is considered to be right-handed just because it can only be played pointing to one's right side...

Many other instruments require more ability and dexterity for the left hand, for example all the strings. But they can be arranged to be played the other way round. Some left handeed guitarists assemble the string on the inverse order.

I would have thought that on a flute board, everyone would know that flutists are ALWAYS RIGHT! (handed or not)

I doubt this if you are referring to tuning...

I understand Lera was referring to mixed-handedness. I was curious about this condition and found a self-made test to check dominance here: http://hunternuttall.com/resources/handedness/

In my case, the result is +1.0 (pure right handed)

It would be interesting to know if there is a higher level of right, left or mixed-handedness among musicians than in the general population. If you find it interesting, post your own results here.

<Added>

The U.S. population breaks down like this:

Strongly right handed: 55 percent
Mixed right handed: 35 percent
Mixed left handed: 7-8 percent
Strongly left handed: 2-3 percent