Shortes and fast transport from Kunming to Xiaolan, Zhongshan

Based on your requirement, here is my suggestion:
take a train from Kunming to Nanning in around 13 hours. Then transfer to a bullet train to Guangzhou. After arriving at Guangzhou South, change to a high-speed light rail to Xiaolan directly and it takes around half an hour.

As for the train timetable, you can search on the train page in this website. The fare is as follows:
Kunming - Nanning: CNY208 and CNY315 respectively for a hard sleeper and a soft sleeper
Nanning - Guangzhou: CNY169-172.5 for a second class ticket and CNY202.5 for a first class ticket
The light rail to Xiaolan costs CNY25-35.