K. und K. (also expressed as K.K. and K. u K.), means Kaiserlich und Königlich. The expression means "Imperial and Royal" and tends to refer mostly to the time of Kaiser Franz-Joseph of Austria who was then Kaiser of Austria but also, I think, King of Hungary. So K.u K. navy, means the Royal Austrian Navy of this period. The same term attaches to many other government departments and officials, even the Royal hunting guides.

Admiral Horthy played a key role in getting chamois to New Zealand, he being the Austrian Kaiser's aide-de-camp when Ritter von Honnel returned from a visit by the naval ship Panther to New Zealand. Vom Honnel conveyed the NZ government's keen desire to obtain these animals, and Horthy, a keen hunter, was able to confirm the suitablity of the Southern Alps as he too had been on a similar trip previously. There's a new book out "Chamois-a New Zealand Hunter's Handbook" that describes some of this history this further.