Demo
From left to right: normal, horizontal flip, vertical flip, both flips. Flipped icons are incorrectly positioned and part of the icon is cut off.
obj/test
icon = 'Icon.dmi'
icon_state = "test"
// These can also be made as instances in the map editor.
vertical_flipped
transform = matrix(1, 0, 0, 0, -1, 0)
horizontal_flipped
transform = matrix(-1, 0, 0, 0, 1, 0)
flipped
transform = matrix(-1, 0, 0, 0, -1, 0)
Same result in 513.