The Falklands are currently a British Overseas Territory, and as such I don't see a problem flying the Red Ensign when putting into South American ports, however I can see your point of view.
I note from this mornings news that the Argentine Confederation of Transport Workers has decided to boycott all British flagged vessels or any flags of convenience used by 'british pirates'.
So, as I said, acquiescing to the first round of harrassment by re-flagging simply invites more.
South America is an important emerging market for several key industries in the UK. We cannot afford to be harassed like this; Kirchner's whipping up of Mercosur is a major economic attack against us and should be viewed as such.