Air Asia flies weekly to Puerto Princesa from Manila, Clark, Davao, or Cebu. I would personally choose Clark International Airport if you’re coming from Luzon because there were only about a hundred people waiting on different flights when we got there as opposed to NAIA’s thousands.
From Puerto Princesa, you could rent a van that will take you to Port Barton in San Vicente. It’s advisable you contact the Inaladelan staff about your plans for a day trip or overnight camping so they can prepare the boat transfer ahead of time.
For hassle-free van transfers and personalized tours, get in touch with Amika Travel and Tours, a reputable travel agency and tour operator and is one of the best travel agencies in Palawan.