Grilling jicama brings out its natural sweetness, but be careful not to overcook it, or it will lose its crunch.
For the kebabs: Puree oil, lime zest and juice, cilantro, garlic, jalapeno, and salt in a blender or food processor. Combine marinade and shrimp. Cover with plastic wrap, and refrigerate 1 hour.
Preheat grill to medium-high. (If you are using a charcoal grill, coals are ready when you can hold your hand 5 inches above grill for just 3 or 4 seconds.) Thread shrimp onto 6 skewers. Discard marinade. Thread jicama onto 6 more skewers. Grill shrimp until opaque and slightly charred, 3 to 4 minutes per side. Grill jicama for 1 to 2 minutes per side. Transfer to a platter.
Make the salad: Toss together chicory, green oak lettuce, scallions, apple, radishes, and jalapeno if desired. Toss in lime juice, oil, and salt. Divide shrimp and jicama skewers and salad among plates, and serve.
Grilled on separate sticks, shrimp and jicama can cook at their own pace to optimal doneness.