Toss cheeses in a medium bowl with flour, cayenne pepper, and white pepper to coat, and set aside. Heat wine in a fondue pot over medium heat until it starts to bubble, about 6 minutes.
Stir in cheese mixture, a little at a time. Stir in kirsch. Continue to cook, stirring, until cheese has melted, 6 minutes. Stir in lemon juice. The mixture should be smooth and almost bubbling. Transfer pot to its stand set over a burner for up to 1 hour. Serve immediately with bread.