For a distinctive Kirin (in case someone *koff koff* wants to do something with both a that and a Giraffe), my image searches have come up with a dragon-unicorn, sometimes (this being the case for my models/icons) with the single horn headed straight back off the forehead.
(That said, for some reason my current search is bearing out your description, even though my earlier searches showed mainly my latter one.)
Also, since you have a Flamingo (1,6), you might as well have an Ibis (1,5).
Anything else I can think of would get too little use to be worth the work.
For a distinctive Kirin (in case someone *koff koff* wants to do something with both a that and a Giraffe), my image searches have come up with a dragon-unicorn, sometimes (this being the case for my models/icons) with the single horn headed straight back off the forehead.
(That said, for some reason my current search is bearing out your description, even though my earlier searches showed mainly my latter one.)
Also, since you have a Flamingo (1,6), you might as well have an Ibis (1,5).
Anything else I can think of would get too little use to be worth the work.