Apparently this flag is used by the British Antarctic Survey who operate from bases in the territory and other nearby UK territories, as well as from the survey's headquarters in the United Kingdom. From what pictures I have seen the survey seem to prefare the Union Flag rather than the BAT flag. Both painted on bases and as a physical flag:
Perhaps this is because the flag is impracticable, the fact the complete coat of arms is used seems strange. My redesign of the flag is quite different:
As flags are designed to be seen the use of white in a very white place seems strange, so a light blue is perhaps a better colour to use, as it still reflects on the climate but won't be completely invisible. The use of a symbol symbol like a snow flake is also a much more practical symbol than a coat of arms.
I have also designed flags for some of the regions of the territory mainly the islands and Ellsworth Land and Queen Elizabeth Land on the mainland:
Alexander Island
Adelaide Island
Signy Island
Ellsworth land
Queen Elizabeth Land
Queen Elizabeth land was named after the Queen to celebrate the diamond Jubilee, hence the diamond pattern on the flag and inclusion of the crown.
Ships of and working for the British Antarctic Survey fly a blue ensign with the BAT arms in the fly:
My re design
The snow flake could also be used as the roundel on survey aircraft rather than the map logo
or
Please feel free to comment