DISCLAIMER: I DO NOT OWN THE HOBBIT
It was common knowledge that Kili braided Fili's hair; moustache and all. From the time Kili could close his tiny fingers into a fist, they were tangled in the warm golden stands that hung like a halo about Fili's head. Then as he grew older, Kili took comfort in braiding Fili's hair. When he was scared in the dark, he braided Fili's hair. When he felt nervous; he braided Fili's hair. When he needed to feel safe, he braided Fili's hair. As a result Fili had the neatest kept braids in the entire company and possibly the whole of Erebor.
It was common knowledge that Fili could not braid hair to save his life. Sure he could swing a sword, flick an axe with amazing power and throw a knife with deadly accuracy. But when he took those strands between his fingers, he suddenly became extremely clumsy and the braids ended up looking like he just wrapped the locks of hair together quickly and hoped for the best.
It was less common knowledge that Kili would not let anyone else braid his hair except Fili. Everyone just thought that Kili had that kind of hair simply would never stay in a braid. Or maybe because he was so vibrant that his hair just kept loosing. But that wasn't true. Kili's hair looked amazing in braids and held better than even Thorin's. But Kili wouldn't let anyone but Fili braid his hair. No one knew of the long hours that Fili sat doing his best to braid his brother's hair, loosing and re-plaiting over and over until his hands were tired and his fingers felt like they could not move again. And each time the braids looked the same; like just messy tangled stands thrown together haphazardly. And each time Kili would either stand in front the mirror or hold the braids up to the light and proclaim them perfect.