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Your answer depends on where on Antarctica you want to go.
Be aware that there is no commercial air service to anywhere on the Antarctic continent. You can, however, fly to New Zealand, Australia, Chile, Argentina, even South Africa, and from there, charter private transport to your Antarctic destination.
There are many many small airports in Antarctica. The one that seems the most popular for tourism is King George Island. Considering you will be flying direct from Winnipeg to Santiago, Chile - 12.5hrs, then from there to Punta Arenas, Chile (where it seems charters fly out of to Antarctica) which takes about 3hrs, and then to King George Island - 2 hours, your total flying time would be 17.5hrs.
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