Now the current flag of the Falkland Islands approved by the Ministry of Defence and used by the Islands Government is this:
It is a British Blue ensign defaced with the Islands coat of arms. A red ensign version of is used on Civil Ships registered in the islands.
Now if the islands did become independent I think it is more than likely they would continue to used this flag. Same way Fiji and the cook islands kept their flags. But if they decided to change to a new flag or again alternatively if they change to a different flag like Gibraltar I propose a design featuring the coat of Arms on an uneven Blue and White striped field.
The shield is less prominent and placed in the canton
Now if the islands go independent the elected leader the chief executive would become the national leader and like any nation would deserve a personal flag:
A relatively simple flag an equal blue and white field with the island coat of arms in the centre. Assuming that they stay in the Commonwealth they would likely keep the Queen as head of state and therefore keep a governor or representative of the Queen. The current governor's flag is the standard design with governors of all UK territories. A union flag defaced with a wreath and the territories coat of arms:
My designs for a new post independence governor's or Royal representative flag are:
The other version is based on the flag of the Chief Executive but the coat of arms is flanked by the Royal Cypher
What about the flag of the armed forces? Apart from the UK military personnel who regularly are deployed there is a small territorial unit of local volunteers in the Falkland Islands Defence Force(FIDF), which is funded and equipped by the local government. I have been unable to find out if they have a flag and if so what it looks like but they do have a unique cap badge. So I based a possible flag on that:
It clearly has the badge in the centre on the a field that resembles the badge and the colours of sea, air and land forces behind them. This unit operates on all 3 fields and so would do more so if independence was given. Which leads on to what symbols would be used on the water and in the air? The naval section FIDF I think would fly their own ensign on patrol craft:
These are the Naval section flags for used at sea in ensign form only hence the crowned anchor. It appears I am not the only one thinking what if? As I have come across these aircraft roundels on the internet(not my design):
All just a what if situation for fun. I certainly enjoyed making these designs.