In a small saucepan, add butter and flour.Stir to combine for 4-5 minutes. Keep stirring the mixture to avoid the butter from sticking or browning.
Add white wine to the mixture and bring to a simmer. Slowly add in different grated cheeses in small handfuls. Stir until cheese is melted and repeat until all cheeses are integrated.
Transfer cheese mixture to a fondue pot. Keep warm with a low flame so cheese can remain dippable.