This is Kate Clark's fingering table for the Haka.
Better to have the third hole slightly open for a in the second octave!
Now let me give the Haka information from the Langwill index 
The Haka flute is a conical flute with one key. However, it clearly is a predecessor of the real baroque flutes. It is only slightly conical and the key is tiny.
This is a very large flute in comparison to baroque flutes. It is …76 cm. long!
A baroque flute is conical from about 19mm. to about 12.5 mm. The Haka flute only is conical from about 19 mm. to 16.5 mm. It is conical but just. This implies that the flute does not give an octave higher by over blowing for a number of notes such as b1 where a normal baroque flute does. In other words fingering wise it behaves like a Renaissance flute. There are only three flutes from the period before the Hotteterre type French flutes.
The Assisi flute, in Assisi, the Lissieu flute in Vienna and the Haka flute in the Ehrenfelt collection in the Netherlands.
The Lissieu flute does not have a key, the other two have a key and are remarkably similar in form but the Haka flute is much longer then the Assisi one. The Assisi flute does not have a mark. The Assisi flute is from about 19.5mm. to about 15 mm. , so also renaissance.
The Haka flute is beautifully turned and form wise in very good equilibrium to my taste. Why were there so few flutes left from this period? We may never know.
It is not clear when Haka made the flute. However there was a good connection between Paris and Amsterdam. In Paris at the end of the eighteenth century the Hotteterre flutes were already in fashion, they are real baroque flutes.
It therefore is unlikely that he would have made this flute as late as the end of the eighteenth century because it still has a renaissance fingering. My guess would be that he tried it somewhere around 1680 or earlier.
Establishing the pitch of a particular traverso often is the topic of a discussion. Basically three issues are involved.
-what do we call the lowest note
-where do we put the cork
-establish the pitch of a/1.
The cork in my opinion should always be put at the position where the octave and the second octave of the lowest note are exact. If we do this for the Haka and were to call the lowest note a “d” it would be about 370 Hz (me playing, much lower if Kate Clark plays). If on the other hand we were to call the lowest note a “c” it would be 415 Hz = 370*2**1/6 for “b” it would be 440. This is a nice coincidence because it means that the Haka is usable with our present standards (Kate playing this is again questionable)!
We may wonder why Haka made the flute conical. The following reasoning may be interesting in this connection. I do not think that wanting many different new properties for the flute at the same time is logical. Therefore we may wonder what the main new aspect is. I think that the e flat in the second octave with the help of the key and seventh hole is a logical choice. This seventh hole is very small. He somehow decided to use a small oboe-like key. So if we drill this hole in about the same spot in a flute that was wider at that spot the hole would have to be even smaller. But then the hole would not function any more. Therefore the single reason for making the flute conical may have been to have a narrower bore at the spot of the e flat hole!!! Moreover, about two centuries later Boehm discovered that he did not need conicity if he could place the finger holes where he wanted with a size he wanted, more or less of course. He made the flute mainly straight. This points in the same direction. In between there have been very conical flutes with quite large seventh hole nevertheless!
 The New Langwill Index. Tony Bingham London, ISBN 0-946113-04-1