Can I catch a flight from Hong Kong to shenzhen and how long of a flight is it?

Well, there is no direct flight that runs between these two places beacuse of the short distance.
From HK airport, you can take direct ferry or long-distance bus to SZ.
If you are in HK downtown area, just take East Rail Line to arrive at Lo Wu Station, then pass the custom and enter SZ.

The duration depends on where you start. You need to tell the starting location, then I can give the extimatate duration.