I'll assume you meant "area beyond the south pole". Your Adm Byrd video is another complete refutation of your flat earth assertion. First he mentions the south pole. There is no south pole in the standard flat earth model. Then Adm Byrd mentions this unexplored area beyond the south pole that is about the size of the United States.
The United States land area is 3.797 million mi². The shoreline of a flat-earth antarctica is going to be the circumference of a circle with a radius of 11,100 miles (approximate distance from north pole to coast of Antarctica), which is 387,076,536 miles long. Let's say that half of it is already explored, and the other half, the part that Adm Byrd (in 1950s when the Longines Chronicles were aired) said was the size of the United States, is the same size as the explored half (I think this is being generous to your argument). Together they are 7.594 million mi². Dividing by the radius above, the potential size of Antarctica all along the coastline is......
Wait for it......
1.24 e-3 inches wide! In case you didn't quite get that, the width of Antactica, as determined by one of America's greatest explorers, when coupled with the nominal flat earth model is only 1/1000th of an inch.