The flag hoisting is reserved for the birthdays of the following people:
- The Sovereign (the Queen)
- The Sovereign's Consort (Prince Philip)
- The Sovereign's children (Prince Charles, Prince Andrew, Prince Edward and Princess Anne)
- The wives of the Sovereign's children (Camilla and Sophie)
- The eldest son of the Prince of Wales (Prince William)
- The wife of the eldest son of the Prince of Wales and his spouse (Kate)
Harry is not the Sovereign's son or the Prince of Wales' eldest son, so his birthday is not in the list.
When Prince Charles becomes King, that will automatically change.