The docs claim that flsgn is “like sgn … but restricted to flonum input.” However, the two functions behave differently for -0.0 and +nan.0:
#lang racket
(require math/flonum)
(flsgn -0.0);-> 0.0
(sgn -0.0) ;-> -0.0
(flsgn +nan.0);-> 0.0
(sgn +nan.0) ;-> +nan.0