When you see that Zachary Brown served through the Second Angl0-Dutch War, and fought in all the major battles, it seems clear that his problems in the First Anglo-Dutch War were not representative of what sort of naval officer he was. King Charles II, the Duke of York, Prince Rupert, and the Duke of Albemarle generally did not keep incompetents around. A nasty feature of the Restoration navy was that if you were someone's "favorite", it could still happen, although it was not very likely. I'm not sure if I could give a counterexample. I would need to study A Distant Storm more closely, to be sure.
I am relatively sure that Zachary Brown took part in the Battle of Plymouth and possibly the Battle of the Kentish Knock, before his mishap on the way to join the fleet, after the Battle of Dungeness (which he had missed). I will check this evening, as I don't have access to my copy of Anderson's article about fleet lists.