I have flight from Beijing to KMG at 3:40pm on a Friday. I stay at China University of Mining and Technology. What is best way to get from University to airport, T2?

From your school, you can take a taxi to reach Zhongguancun Fourth Bridge (Zhongguancun Sihaoqiao) to take the airport shuttle bus line 5 to reach the airport directly.
The bus journey takes about an hour. Upon reaching the airport, you should follow this process: check-in - Go through Inspection & Quarantine or Entry & Exit Frontier Inspection - Security Check - Customs Inspection - Waiting & Boarding
You need to arrive at the airport 2 hours before the departure time to go through the procedure.