The rank of Captain is assumed by Nancy and John (SA). Following the War between the Swallows and Amazons Swallow becomes flagship, and John therefore becomes Commodore, but this title is never used after this, and Nancy does not seem to relinquish any command over the others.
In the Norfolk books, Tom and Joe hold the rank of Captain; the title is seldom used, though (CC9) says The Captain of the Death and Glory (Joe) was looking over his shoulder. And Mrs Barrable is bestowed with the honorary title of Admiral; Starboard says just tell the Admiral ..... Well, just look at her fleet (CC9).
Ted Walker is a Commander in the Royal Navy, who seems to gain a promotion to Captain in Secret Water. In Missee Lee Titty says to Miss Lee that John is good at mathematics, and doesn't really need Latin. John says that is because I'm going into the Navy .... Like Father. He then tells Miss Lee that their father is a captain in the Navy, and predicts that he will be an Admiral when he retires (ML16). Roger says he is a real captain, not like Captain Flint. I expect you've seen his ship. He was stationed at Hong Kong. Miss Lee exclaims Gunboats!, tells them to tell no-one, and says ..... Better I fo'get.