Preheat grill or broiler. In a mixing bowl, gently stir together beans with 2 tablespoons of the olive oil, 2 tablespoons of the balsamic vinegar, the red pepper flakes, basil and garlic. Season lightly with salt and pepper.
Halve the radicchio from top to bottom and place on an unoiled grill or under the broiler. Cook until wilted, about 3 minutes per side. Cut each half in half again to form wedges. Cut the core piece out and separate the leaves. Toss the leaves in a bowl with the remaining 4 tablespoons oil and 4 tablespoons vinegar, then season to taste with salt and pepper.
Arrange the radicchio leaves on four plates like the fingers of a hand. Spoon the bean mixture onto four freshly grilled bread slices, place one slice in the middle of each salad and serve.