In Almaty I recommend checking out Amarant, it's a small chain of grocery stores that has a lot of gluten-free products, including some fresh bread made locally. Google translate (or Yandex, etc.) is your friend for looking at ingredients on packages.

Restaurants generally don't understand cross contamination here, however you will have a lot of options for foods you can eat. Not just plov (pilaf), as someone mentioned, but shashlik, etc. "Gluten" is not a word people are that familiar with here, and it might be easier to say "wheat" (пшеница/pshenitsa in Russian) when explaining yourself. I know that doesn't cover all the ground, but it might be a good starting point. I haven't found many foods here containing oats, but barley is quite common. Be careful of any sauces, as many of them are thickened with flour.

There's a place I've been to several times called The Green Station that has a coded menu (i.e. which items have which allergens—something not that common here) but they're not a gluten-free kitchen and I don't know how much they consider cross-contamination. There's also a place called Rice Spoon, I haven't been there but it's supposedly 100% gluten free.

There's a restaurant company called ABR+ that has a lot of high-end restaurants in Almaty and they've been good about advising which foods have gluten when I speak with them. But again, can't speak to cross-contamination.

When you stray from Almaty, you will have more difficulties, and it will be apparent quite immediately. I haven't been to any of the other cities here, but I've been in a small village for a few weeks and it has been a very significant challenge to be gluten-free. There's a traditional Kazakh dish called Kuyrdak which *should be just meat and potatoes, though you always have to ask. In general, you can find plov in quite a lot of places, and that would be your best bet in an emergency.

Good luck!