Does anybody know, if I can buy an iTunes gift card at any of the Apple stores in Kunming?
You mean all the fake Apple stores? I don't think even the sole authorized reseller in Kunming would have them.
Best to try online. Maybe amazon.cn taobao ebay or maybe apple hk or apple cn sites.
I haven't checked for Apple, but I checked for Canon once. I contacted the US store via their web site and they gave me a link to the official resellers in China.
So, Apple might be able to do the same. Look them up online and ask them if there's an official Apple retailer in Kunming.
Otherwise, you can buy online from amazon but you have to pay shipping.