Speaking from personal experience, you need to check the schools yourself first - there are many gates and hurdles to overcome - from residency, household registration (if the kids have Kunming hukou) etc ad infinitum.
Typical class sizes from primary to middle schools are 60-70 students. The standard class size is supposed to be 30's to 40's and Kunming is doing a lot of high density housing without addressing the school issues in the inner cities.
You should also check the schools' overall test results and rankings - as certain schools have a high density of lazy students with no intention of higher education. In fact - in china most students don't even think about higher education - they're just prodded along like mindless livestock.
As foreigners or children of foreigners - they'll be exposed to extensive bullying - especially if you're American.
Finally - the schools may do this delaying tactic - as a foreigner - they'll still try to extort bribes from you despite the substantial government crackdowns on corruption - nowadays - you'll have to go through a "proxy" to launder the solicited bribes (can I actually say this publicly?).
Theoretically - every child is supposed to attend primary and middle school - but my children with non-yunnan hukou were blocked from attending any of the schools in our neighborhood - so I sent them and wifey out of the province to wifey's hometown, as I refuse to pay bribes to government employees...disgusting behavior.
If you work for a company - they might write a letter of introduction to the education ministry - and then have the education ministry write a letter of introduction to the neighborhood schools you'd like your kids to attend.
We specifically instructed our children's teachers to NOT mention they're xxx country citizens to avoid bullying. Teacher announced it proudly every year in front of the class...let the bullying begin...again...may the fleas of ten thousand camels infest her for the rest of her life.
So in short - we had an extremely negative experience with local schools in kunming while trying to blend our kids into school (they're putonghua native level speakers with a smidgeon of kunminghua). Abysmal failure.
Other's may have more encouraging experiences...I sincerely hope...I have absolutely nothing positive to say about the culture and behavior of the school's administration or the schools themselves.
One piece of advice - look for schools with younger administrative and teaching staff - they're usually (not always) significantly more professional and responsible.
My daughter's former school principal was invisible for years until she was finally arrested for corruption (siphoning off construction funds to her personal banking account). Her new principal - younger guy (like early 40's?...kids...sheesh) walks the school grounds all the time and is highly visible. Seemingly an extraordinarily pro-active principal...hopefully the sign of better things to come but too late for my kids...