Voice Lines from the wiki indicate she's trying to make friends with Kirishima.
Either one works for me and depending on luck and artist prefernce could be one leading to the other. American ships tend to be the younger ones in most cases and Kirishima and Dakota are or were part of the last battleship to battleship battles so we have material for both outcomes.
Plus pretty sure Kongou would be just fine with it
I'd prefer Kirishima trying to prove she's better than the Black Prince(Princess?), and South Dakota just not caring.
There is no possible way a personification of South Dakota could not care about looking 'cool', seriously go look at her career and how her crew behaved. Sodak had a case of small man syndrome just as pronounced as her stubby length.
Tadaaah!Kirishima!!
Look at this, Kirishima!!Kirishi-Her intellect decreases in front of Kirishima.How about that!
Heheh♪