From the looks of it, it's going to be based on Pirates of the Caribbean: At Worlds End. Characters appearing in this trailer are Captain Jack Sparrow, Joshamee Gibbs, Hector Barbossa, Elizabeth Swann, Will Turner, and Tia Dalma.
Non POTC characters included in the POTC segmants are Sora, Donald, Goofy, and Luxord .
As a guess, I imagine Davy Jones, Cutler Beckett, James Norrington, Sao Feng, Bootstrap Bill, and the other crewmembers of The Flying Dutchman could make appearnces as well.
Davy Jones makes thematic sense in the Kingdom Hearts series, as the situation with his own heart closely resembles that plight of The Nobodies , who are the bodies of those who have lost their hearts to darkness.
As a side note: The POTC franchise will receive additional representation in the form of a merchanic known as "Attraction Flows", where Sora and Co. go on an automobile that resembles an attraction vehicle from the Disney Theme Parks, in this case a boast from the ride.
Also, Goofy mentions that the Sora "...always did like (the POTC) world", known as "Port Royal" in Kingdom Hearts II.
This looks like it could be one of, if not the greatest representations of Pirates of the Caribbean in all of video games.