I am staying in Kaifeng and I'm flying from Zhengzhou Airport onwards to Chengdu.

Well, according to your departure time, you are suggested to take the direct coach at the intersection of Songcheng Road and Jinming Avenue, arrive at Xinzheng Airport. The earliest schedule is at 05:10. It costs CNY 40 per person.
Generally speaking, you need to arrive at the airport two hours in advance. And the coach takes around 2 hours on the way. Thus you need to take the earliest schedule. :)