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That failure to chamber is most likely caused by an extractor that is too tight. It could also be helped along by a rough breech face. One other possibility is your magazines. Does the problem happen with all mags?

Kimber put a new slide on your frame, correct? Take the pistol apart and put a cartridge up against the breech face and under the extractor, the way the pistol does when chambering a round. The extractor should be only tight enough to keep the round from falling out on its own. There should be a little movement when you shake the slide, but the round should not fall out. If it is so tight that the round is held flush to the breech with no movement, it needs to be adjusted.
It is fairly simple to adjust but if you have never done this yourself, don’t. Let your gunsmith do it. You have to pull the extractor out of the slide and bend it a little. It is easy to overdo it and ruin the extractor.

You should also check the breech face of the slide for any roughness or possible flow from the firing pin channel. If you find something the easy way to smooth it out is to take some 600 grit Emory cloth wrapped around a popsicle stick and polish it out.

There is probably nothing wrong with your barrel. Is it a new barrel or your old barrel that was fitted to your old slide?