In a large mixing bowl combine the sliced tomatoes, 1/4 cup of the oil and the torn basil leaves.
Drop the pasta into a pot of generously salted boiling water.
While the pasta is cooking heat the remaining 2 tablespoons of oil in a skillet over a medium flame and add the red pepper flakes and sliced garlic. Cook for 30 seconds and add the Figs to the pan. Cook until the Figs begin to breakdown, about 3-4 minutes. Remove from heat
Once the pasta is al dente drain it and add it to the bowl with the tomatoes. Add the cheeses in immediately and toss well to coat. The heat of the pasta will begin to melt the cheese.
Pour the oil and Fig mixture over the pasta and mix together. Serve chilled.