I will be flying from Bangkok to Phuket, taking the ferry to Phi Phi and then returning a few days later to Phuket and flying to Chaing Mai. I'm not sure which flights to book on for the 13:30 ferry to Phi Phi from Phuket and 9:00 am ferry back to Phuket. (Flights would be from Bangkok to Phuket and Phuket to Chaing Mai.
Would appreciate any advice.

I would book the earliest available flight in order to be able to get into Phuket and get to the ferry in time, probably by 1pm a the latest. If you're booking with one of the discount carriers especially, factor in at least an hour delay. I wouldn't book any flight before 4pm from Phuket on the way to Chaing Mai. The ferry may take longer than expected depending on the weather and you still need to get to the airport and have enough time to check in and go through security.

also allow for rough water or storms

Agree 100% with advice above.

The road transfer between Phuket airport and Rasada Pier takes around 45mins, by car. Immigration at Phuket can be horendously long.....on our last visit it took nearly 1 hour. So DO NOT cut it fine. If your budget can stretch.....then take a speedboat transfer....much less stress and our preffered method.

I agreed with LeighTravelClub and some online booking has Airport Transfer booking service,you won't worry about Arr or Dept time because they will send you an e-mail that where and what time they will pick up,you haven't missed your Flight.