Cockatrice = a dragon with a rooster's head. Why cannot it fly?
Cockatrice has 2 usual depictions:
1. A dragon with rooster's head with petrifying gaze.
2. A variant of grounded harpy, which can't fly.
To avoid confusion, i assume this game uses the second depiction, which actually fits the game aside from the artwork.
As for creatures with petrifying gaze, there are bailisk, catoblepas, gorgon, and such. Which is (again, assumed to be) not the case with this card.