Thread the mushrooms, zucchini, squash, orange bell pepper, green bell pepper and onions onto separate skewers.
Mix the Italian seasoning, salt, black pepper, red pepper flakes and 1/4 cup of the olive oil in a small bowl. Brush the kebabs all over with the oil mix.
Preheat a grill pan over medium-high heat. When it is hot, grill the kebabs, turning as needed, until grill marks form and the veggies have softened, 8 to 10 minutes total.
Using a fork, push the hot vegetables off the skewers onto a serving platter. Drizzle over the lemon juice and remaining 3 tablespoons olive oil. Toss to combine. Sprinkle over the crumbled feta and lemon zest. Top with the oregano, mint and parsley. The salad can be served warm or chilled.