Kappa paints its equipment in classic Star League colors: white and gray, with blue and silver trim.
Per FM:Crusader Clans, page 127.
All Adder 'Mechs and fighters bear the Clan insignia on the left arm or wing and right leg or empennage. Galaxy insignias are displayed on the right arms or wings and left legs or empennages, while Cluster insignias are worn on the right torsos of 'Mechs or the fuselages of fighters.
The Galaxy's insignia is the Greek letter Kappa over the Star Adder emblem.
Per FM:Crusader Clans, pages 118 and 127.