'Flying foetus' is associated with the following type of presentation of the fetus:

In 5 percent of term breech presentations, the fetal head may be in extreme hyperextension. These presentations have been referred to as the stargazer fetus, and in Britain as the flying foetus. With such hyperextension, vaginal delivery may result in injury to the cervical spinal cord. Thus, if present after labor has begun, this is an indication for cesarean delivery. Ref: Leveno K.J., Hauth J.C., Rouse D.J., Spong C.Y. (2010). Chapter 24. Breech Presentation and Delivery. In K.J. Leveno, J.C. Hauth, D.J. Rouse, C.Y. Spong (Eds), Williams Obstetrics, 23e.