Hi, Ocarina maker here! This is a genuinely interesting idea, and some Ocarina like the Goslings do have a double keying with a single finger.

Sadly with English Vessel Flutes (4/6/8 holes) the holes need to all be roughly equidistant from the center of the chamber, which makes a two finger setup ergonomically complicated while keeping a tangential fipple. It is also very desirable to use the pads of the fingers to cover the holes, making a good air seal is tricky with the middle of the finger. On ergonomics, it is also worth mentioning some Ocs get quite big as well! My largest 6 hole is almost 300mm wide, my fingers are not quite long enough to span this...