Bring a large saucepan of salted water to a boil. Add the farro and cook until tender, about 20 minutes. (If cooking whole-grain farro, it will take 30 minutes.) Drain well.
Combine the olive oil and red pepper flakes in a large serving bowl. Add the tomatoes, mint, parsley, radishes, cucumber and lemon juice and stir to combine with the oil. Toss in the farro while still slightly warm. Add the arugula and toss. Top with the feta and season with salt and pepper.