I suspect this is a High Pitch instrument. I sent the seller a message requesting sounding length and C#-Eb measurements a week or so ago, but they have not replied.
By the way, if you look at Terry McGee's page on
A Guide to the Lengths of Flutes there seems to be a bit on an anomaly in the figures presented for the lengths of Rudall Carte early model vs later High Pitch cylindrical bore flutes. The anomaly is that the overall length, and the min emb to A, quoted for the High Pitch flutes are longer than that for the earlier models, which I initially assumed were lower pitch flutes, because they had longer sounding length and C# to Eb lengths. However, now I presume this data means that there were two different models of High Pitch flutes, the earlier ones being even higher pitched than the later ones if the tuning slide was fully compressed.
Anyhow, according to Terry's page, the overall length of the earliest Rudall Carte cylindrical bore flutes is 639 mm, the later High Pitch ones 654 mm, and their 1940's flutes, which are presumably modern concert pitch, 678 mm. This flute for sale on eBay has an approximate length of 640 mm, making it very likely a High Pitch flute, even taking into account the missing end cap.