If you've tried to manage eating out and describing complex allergies in your native tongue, you'll likely appreciate the challenge in negotiating a celiac diagnosis in a foreign language. I must therefore plug the following restaurant, both for its calibre and for being accommodating.
Given my Japanese literacy, it is only known to me by its url, http://kyoto-rokkon.jp/ as found on their business card. It is located on the border between central Kyoto and Gion, on a road running parallel to and just on the west side of the Kamo-gawa river. It might be Kawara-machi-dori, just a little south of Shijo-dori (the east-west too generic main shopping drag). The restaurant is small, cozy, and staffed by energetic young gents who confirm each order with vigorous "Hai's" and punctuate each new guest's entry or exit with equally emphatic greetings.
We had omakase, a Japanese tasting menu, and although details of the menu are now fading in memory, it was distinctly fresh, simple, of appropriate (read modest) portions, and creative. Served in earthenware type dishes, it had a very comforting feel. Some of the dishes seemed influenced by bistro cooking, particularly a little mushroom and cheese soup. They also made if gluten free. I even had rice flour tempura, which, at least on our second visit their, was definitely fried in separate oil. Of note, there was still a language barrier. So, although they had a little English sign indicating they catered to allergic types, you still had some work to do. But with a little language card or some rudimentary Japanese (as I had), things worked out.
Give them a try.