Correct. The kinki is not a feature rich unit. No dollar wasted. It’s made to do one thing, pump out two channel audio with clean, focused power.
The best way to bring in headphones would likely be through a dac with multiple outputs. For example, my Dac on my desk, and my Dac/streamer in my system both have RCA and XLR outputs. I could run XLR to the Kinki and RCA to a headphone amp.
Another (more expensive) option is to move to a dedicated line stage and separate power amp, assuming you select a line stage with multiple outputs.
In the Kinki eco-system this would include the EX-P7 line stage and the EX-M7 stereo power amp.
OR
Kinki does make a headphone amp with a preamp out. But I wouldn’t want my primary signal passing through an extra device.