For the King, the first greeting is "Your Majesty," thereafter, "sir."
For a duke, marquis, earl, viscount, or baron who is a member of the royal family, "Your Highness," the first time, with "sir" thereafter. If not a member of the royal family, "your grace," the first time, followed by "sir" thereafter.
When King Edward VIII abdicated in 1936, he was created the Duke of Windsor. His wife, Wallis Simpson, became the Duchess of Windsor (because she was married to him), but King George VI specifically declined to extend the style, "Royal Highness" to her.
Therefore, the appropriate form of address was "Your Highness" for him and "Your Grace" for her.
The Duke of Windsor required members of his household to address her as "Your Highness" however, but that was not technically correct.