Get a team of at least 5 people all which enough flags and guns (to protect against attacks, most likely from animals, and to hunt) to carry the Revolution and stay safe.
Get a macronation to support the Revolution and to recognize it (it can be before, during or after the Revolution). Put your bets on a country that doesn't have an Antarctic claim or claims and is similar in government (like Venezuela)
Antarctica is a place for tourism, more than you might think. Do this at a time where they will be less tourism. DON'T DO IT ON WINTER, IT'S TOO COOL! If you can't find such a time, do not grab attention until the end of Revolution!!!
Put the flags across Antarctica, you don't have do it all at once.
Tell the world about the Revolution, Step 2 would help in making sure you and the new Federated States are safe.