Another common image for Kaladin is Vev, with the attributes Loving/Healing. Almost all of Kaladin's past scenes have her, as well as many of his present ones. She always seems to be in the chapter heading when Kaladin is trying to heal someone, or when his old surgeon side comes out.
Maybe sometimes a Herald image was chosen to match a quality or qualities being displayed in that chapter, which, in Kaladin's case, was healing.
Also, the most telling image for Kaladin's order specifically would have been the chapter "WORDS", where he says the Second Ideal specific and unique to his Radiant Order. In that chapter, it is Jezrien's image alone that appears, linking Kaladin with the 1st order and the attributes Protecting/Leading. (In fact, the words "I will protect those who cannot protect themselves" suggests the attribute of protecting for Kaladin's order.)
Thus, I would highly suspect that Kaladin is of the 1st order.
Of course, the question now is, what common thread runs through those Kaladin chapters where Talenel's image appears? (as healing runs through most of the Vev chapters)