Combine Cheddar cheese, Swiss cheese, flour, salt, and black pepper in a bowl.
Rub cut side of garlic clove around bottom and sides of fondue pot.
Pour beer into fondue pot and slowly bring to a simmer over medium-low heat, about 5 minutes.
Gradually stir cheese mixture into beer, adding small amounts at a time, until cheese is melted and blended, 10 to 15 minutes.
Stir hot pepper sauce into cheese mixture.
If mixture gets too thick, reheat and/or add a little more beer.
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