BBs:
KM BBs are all about pushing, at least when its a fight between equal tier ships.
They are the best ships for line fights. KM isn't the one that finishes the enemy with 1 hugh blow but wears them down. Always be on guard. KM BBs want to be loved. They want all the attention that you have. Just one moment of abstartion will kill you.
Another note: dont trust those guys telling you KM is all about running. KM BBs that just run away are dead meat.
At lower lvls KM BBs are extreme fast allowing some rushing and grabbing damage. Furthermore the amazing AA makes the lower lvl grind rather enjoyable. I recommend you to run M-pro,hipper,eugen with KM-40s on the r-slots or Dland, P-Pro with 4.1inch duals AA guns on t-slots. Even for Moltke i recommend the KM 40s on r-slots and HHs on t-slots.
Checklist for KM BBs: pushing, slingshoting, 110% attention.



CVs:
I am not a fighter player but as far as i know thier fighters are very solid.
DBs are KM players bomber of choice. 2nd highest damage. Only SN has more.
TBs aren't a good choice. While they are dureable, they dont really pack a punch. RM and UK are better at this.
A small extra tip: KM CV5,PCV,CV6 are a good AA-plattform, too, making it easier as bomberwhore or low lvl fighter cv to defend against superior CVs.



Subs:
Unique proxy torps. Very good in SS vs. SS and SS vs CA/CL/DD/FF. For hunting BBs there are better nations. though KM isn't totally useless for that.
Since KM has a rather low number of support-slots i would recommend to get a BB5 before starting a ss crew. Otherwise it will be a extremely hard grind.

KM has the unique ability to give you ample opportunity to hit ships (work on your aiming skills)... as any other nation quickly sinks opponents because they can cause damage with the great shell damage rates, meanwhile, with KM, you'll get to land salvo after salvo on ships and they will stay cruising along with their health still in the green..

which leads to another KM strength... you don't have to worry about searching the maps for ships at the end of a match because you will most likely be one shotted (maybe 2 shotted) because you have paper ships that are easily sunk by other nations.

They say that there is a KM speed advantage but it is so miniscule as to not matter... another rumor is the KM range advantage... the problem with that is that the advantage is super tiny (almost non existant) and that is under idea conditions... in game with many ships moving in and out  and coming at your from all angles you are hardly ever in a position to outrange ships and will quickly succumb to ships that out damage you because they hit harder and out last you because they have better damage protection/defense.

Of course... everyone else slingshots also... thus the range advantage is still negligible.

KMs strength lies in the fact it has a small extra amount of range over it's targets. the thing that adds to that strength, is the fact that they reload way faster at equivallent shell sizes. there are some ships at level vs level have a stronger range advantage. the final strength they have, is their speed and over heat longevity. their weakness includes toothless fire power and can be destroyed easily. tactics that will work include preemptive strikes with running away in mind. they have weak turning forces in the later levels. so, forethought and planningust go into every move you make.