Combine vinegar, sugar, star anise, fennel seeds, red pepper flakes, 2 teaspoons salt, 2 tablespoons orange juice, and 1/4 cup water in a medium bowl or glass jar; stir (or cover and shake) until sugar and salt dissolve. Add grapes and let sit at room temperature at least 30 minutes.
Toss radicchio in a large bowl with oil, 3 tablespoons strained pickling liquid, and remaining 1 tablespoon orange juice; season with salt and pepper. Transfer to a platter and scatter drained pickled grapes, almonds, and goat cheese over top.
Grapes can be pickled 3 days ahead. Cover and chill.