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Well, it's not a great flag, for many reasons: too similar to Argentine flag, yellow on white isn't a contrasting color scheme, the map is too difficult to be reproduced.
This flag, if used elsewhere, is totally unofficial, as the Argentine department doesn't have a flag. The flag flown by British territory of Falkland Islands is the following (Argentine claim also include parts of South Georgia and South Sandwich Islands and British Antarctic Territory):
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Some proposed flags to the department can be found here, but flags are too generic, plagiarist or badly designed.
My flag proposal is inspired by a coat of arms that gained a competition in 1966 to a new coat of arms for Argentine. The coat of arms below, as well as many others related to the islands, can be seen here.
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My flag proposal is the following:
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The blue-white color scheme is predominant in most Argentine provincial flags, and I decided to follow the pattern to this department. The Sun of May is a symbol of claimed sovereignty over the islands. The symbolism of the waves is very obvious. In a arrangement inspired by coat of arms above, four stars are put on cross, each one representing a island or an archipelago: top (special place) for Falkland, left for South Orkney, right for South Georgia and south for South Sandwich.
Your comments are welcome.
I'd like to remember it's a creative exercise and no way has intentions to show political statements.