I have two different paid accounts with KingsIsle. Why is there only one Captain's Log? I would think that there could be conflicts or lost data if I play on one account and then the other. If a person has 2 accounts, why aren't there 2 Captian's Logs - one for each account?
What Captain's Log are you talking about? The only one I know about is the sub-forum here where One-Eyed Jack and other KI folk tell us what is happening with the game.
As for playing with two accounts, I do that all the time. Most often at the same time. With only one install of Pirate101. And I haven't had any lost data or conflicts even when both instances of the game try to download the same thing at the same time.
I just realised what you are talking about. Those logs are just the information of what happened when you were playing. Is is not read by the game, only written to. There is nothing to worry about in regards to conflicts or lost data.