Is it possible to root the Samsung Galaxy S II without installing a custom kernel or otherwise flash custom firmware?
Why do you want to avoid flashing Chainfire's kernel? From XDA:
This rooted kernel is for the "rooting beginners" and those who want to keep as close to stock as possible. CF-Root takes the kernel from an original Samsung firmware, and just adds root, busybox, and ClockWorkMod (CWM4) recovery.
Rooting voids your warranty just the same as flashing does, and Odin is virtually guaranteed to save you if you ignore the instructions while flashing and screw something up.
You can also re-flash the stock kernel afterwards, which will remove CWM while still leaving you rooted.
Edit: Gingerbreak apparently only worked on test devices.