Not sure the answer to the "how did Vane get to Charleston" question, but as far as landing undetected, if you've ever been to Charleston you know it is a series of islands, rivers and inlets that could very easily conceal a ship.
So now that Jack is no longer worried about being destroyed upon return with the Urca gold, he will soon set off to gather it. I also predict that Vane will also go after it once he secures Flint's ship. And then newly pardoned Flint will be provided one of those war ships to go after Vane to bring him to justice for his piracy. Leading to a massive three-way naval battle for all the marbles (gold).
So now that Jack is no longer worried about being destroyed upon return with the Urca gold, he will soon set off to gather it. I also predict that Vane will also go after it once he secures Flint's ship. And then newly pardoned Flint will be provided one of those war ships to go after Vane to bring him to justice for his piracy. Leading to a massive three-way naval battle for all the marbles (gold).