Only the slide, frame, and some small parts are really stainless steel.
Most small parts and the barrel are hard chrome plated carbon steel.
I recommend buying a jar of JB Bore Paste and some Kroil from Brownell's or a gun shop.
Soak the bore in Kroil for at least 24 hours to soften and loosen the rust.
Then use the JB Bore Paste and Kroil on patches to throughly scrub out the bore per the instructions.
This will remove the rust, but there will be at least some pitting.
This is no big deal, since a lot of guns are badly pitted and still shoot extremely well.
In a small defense handgun the pitting will have zero effect on anything and you can shoot the gun forever with no problems.
If you don't want to go to the trouble of ordering JB and Kroil, just buy a new bore brush, and soak the bore with a bore solvent like Hoppe's #9 for 24 hours, then liberally brush out the bore.
This too should remove the rust.
Note that you should use a new correct caliber bore brush. An over-caliber bore brush just folds over the bristles and doesn't work any better.
Yet another trick is to buy some COPPER Chore Boy pot scrubber pads.
Pull off a strand or two and wrap around a bore brush.
This will also scrub off the rust.
NOTE: Use GENUINE Chore Boy that says 100% Copper on the label. Other brands are actually stainless steel with a copper plate.
These can destroy a barrel.
If it absolutely just bugs you, then consider having Kahr fit a new barrel, or trade it in on a new gun.
Personally, If I had a reliable Kahr I could live very well with a pit or two.