Green’s Dictionary of Slang

flyer n.4

also flier

(US prison) suicide by throwing oneself from an upper gallery in a cell-block.

[US]Maledicta IX 180: Terms provided by him and collected from police, fireman and ambulance personnel slang as to cause of death: […] jumper and flyer (jumped).

In phrases

take a flier (v.)

(US prison) to kill oneself by leaping from an upper gallery.

[US]N. Algren Never Come Morning (1988) 153: ‘If I was here for six more months [...] I’d take a flier.’ To take a flier was to throw oneself over the rail headfirst onto the concrete below.