What does the medical terminology 'flight risk' mean?

"Flight risk" in medical records means "Patient might run away, leave without notice." A risk is a possibility that carries a level of danger of a negative outcome.

So, for example, if a patient is a "Fall Risk", the patient's mental or physical condition carries a level of danger that could make the patient apt to fall if allowed up without assistance.

A patient whose mental or emotional condition carries a level of danger that could make the patient decide to leave or run away, or to wander away (whether with or without pre-planning of the act) would be a "Flight Risk". However, the phrase flight risk is more often used in medical documentation about someone who is on a psych unit or is under police custody while a patient in a hospital.