select count(
flopHandCategory(Hero)=flopset
or fourFlush(Hero,flop))
from game='omahahi', Hero='KK$ds,KK$ss'
(FourFlush is a special function which evaluates to True is the player has a 4-flush on the given street. This can't be obtained by using flopHandCategory because it returns only made hand categories like flopsecondpair, flopbottomtwo etc.)
This counts what you told to, but you should be cautious in your wishes because I guess you don't want to play KK suited not to a king and wouldn't mind flopping anything better than a set

. Also, you probably wanted to do separate calculations for KK double suited 'KK$ds' and for KK suited to a king 'KxKyyz' (x,y,z refer to an arbitrary triple of different suits). So it should be more like that:
select count(
flopHandCategory(Hero)>=flopset
or fourFlush(Hero,flop))
from game='omahahi', Hero='KxKyyz'