You could be having a problem with kimchi because of its fermentation process, unrelated to any spiciness. I used to make my own kimchi, sauerkraut and other fermented foods, and a few of my friends with less than iron stomachs sometimes had some digestive troubles with my concoctions. If you want to be able to handle it, I suggest eating it on your own in small amounts regularly, maybe just a tiny bit at first, slowly increasing. Your stomach will eventually grow accustomed to it, and as a bonus you will have a digestive system that won't hassle you as much when you travel to far-flung places with different standards of food hygiene.