@Calgrad unfortunately, there is some prejudice held against foreigners and people with darker skin in China in general. This includes SE Asians such as Thais (those without Chinese ethnicity) and Malaysians with only moderately tanned skin, the former receiving a bad rap in the eyes of many local Kunmingers according to my Chinese friends. This is not so much because of their appearence (indeed, there even seems to be some negativity towards ethnic Chinese Thais) but probably has something to do with cultural differences and possibly superior cultural attitudes on the part of both parties.
When it comes to black Africans and African Americans etc. the Chinese view is often one of extreme ignorance and occassionally downright prejudice, with mothers regularly shielding their kids once sight of a black person is made, although this is by no means the reaction everyone will give you. Most people will simply ignore you, just like they ignore me given that Kunming is a big city, but if you walk long distances from place to place there will probably be the odd person or two who decides they need to comment on your appearence or something - they'll probably do it behind your back, but that's not necessarily any more reassuring. It must be said that most racism in China is subtle and very rarely involves violence. So don't worry about that - what you will have to deal with are stares, comments and other forms of ignorance, many of which will be quite subtle in nature, but discriminatory nevertheless.
I will never understand the racist attitude by some Chinese that you have to be white to teach English, assuming that's the kind of work you are looking for. However, I think it could be that because China is so homogeneous, and the Chinese are used to associating someone's physical appearence with certain countries, they may not be aware that America, Australia, Canada etc. are actually very multicultural and that there are plenty of non-white people living there who are also citizens of those countries and fully integrated etc. This likely leads to the view that black people are "non-native" speakers and thus not qualified to teach. In addition to this, the prevailing negative attitude towards black people doesn't help either.
Personally, I think there are many people of different ethnic and cultural backgrounds who are very well qualified to teach English, probably much more than I am (I am an engineer, but in the past I did teach a bit of English on the side). For starters, I don't have any teaching qualifications and I don't even like teaching, it's mundane and offers no advancement opportunities, hence my lack of motivation in the past.
Therefore, get out there and fight any prejudice you may encounter! Be self-aware but don't let anyone get to you. Find a job and try your best to ensure that you won't be rejected because of what you look like. Most of all, try to make the most of your experience in Kunming. Like others have said, once people get to know you, the barriers do break down.