To get looked at for the king air, you'll need to have all ratings, maintain an extremely high pass rate, have a fairly clean discipline history with the company (I didn't), ~1200 dual given, over three hundred multi (with the company), over a year with the company, be a stage check instructor, be at tier 4 scale, wait for seniority, and Ideally be on the contract Chinese side.
Now those are subject to change based on need or changing CAAC regulations but that is in general what us current king air pilots had when we got in.