Well, a flageolet, really…
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I’ve come across a few in antique/junk shops over the years. Sadly, they’ve all been really overpriced, slightly damaged and they’ve all sounded really out of tune when I’ve played them. I don’t think it was my playing but it might have been.
I’d like to have one to tinker with, certainly, and that looks a much better example than I’ve than the ones I found.
That’s a pretty reputable shop, and the price seemed reasonable. I can’t imagine something like that could ever play in tune, though. 
Lark In the Morning once had what it billed as a Boehm recoreder, in the used instruments section of its catalogue. Said it had a recorder mouthpiece, and a Boehm flute body.
If you put an Abell high f head on a Boehm piccolo body, it will be very almost in tune. Each octave is in internal tune, but the higher octave is slightly sharp. It’s cool, though.
Dan Bingamon (Jubilee Instruments) makes one I think I remember seeing it on his site the site isn’t working right now though.
I bought one of Daniel’s prototypes. It’s really good. The only problem I have is that the angle my wrists have to be at when holding the flute vertical like that are uncomfortable to me.
I once had a keyed whistle. I still have it, actually. With all those keys on such a little instrument, it sometimes can be difficult to play.
Pretty reputable brand, before anything. A real Buffet-Crampon !
I can imagine these masters of Boehm-system clarinets DID tune it.
Now, to what pitchfork remains open : you don’t know whether you’d get it concert C, or rather a modern Eb, or even D…