It was announced in 1999 that the intention was that Edward would eventually be created Duke of Edinburgh when both the Queen and Philip were dead and Charles was King. This was because then the title would merge with the Crown as the holder of the Duke of Edinburgh title would also be the King. The Edinburgh title, is like most titles, with the remainder of 'heirs male of the body' so the line of succession the Edinburgh is Charles, William, Harry, Andrew, Edward, James.
However, in the scenario I mentioned above, Charles, William, Harry and Andrew all predeceasing Philip then Beatrice would be Queen and Edward would inherit the Edinburgh title directly as the only surviving son of Philip.
But there are also scenarios whereby the Edinburgh title could go somewhere else and not be available for Edward at all e.g. William has a daughter, then Charles and William die leaving Harry as Philip's heir to the dukedom and William's daughter as heir to the throne.
I have outlined some of the possible scenarios that see the title either not reach Edward or reach him directly rather than simply need to be recreated for him here:
http://www.theroyalforums.com/forums/f23/the-future-of-the-duke-of-edinburgh-title-24343.html
The most likely scenario is the one whereby Charles re-creates the title for his younger brother but it isn't automatic that Edward will ever get the Edinburgh title.
I would hope that if one of the scenarios arose whereby Edward wasn't able to inherit the Edinburgh dukedom or where it couldn't be recreated for him that Charles/William would give him another Dukedom, as befits the son of a monarch.