Special equipment: 4 bricks; a rectangular cooling rack
Preheat a grill to 325 degrees F.
In a small bowl, mix the celery salt with a few pinches of kosher salt. In a medium mixing bowl, stir together the butter, red chili flakes, garlic, the juice of half a lemon and half of the celery salt mixture.
Put some of the butter mixture on a spoon and press it under the skin of the chicken from the cavity side. Continue to work more of the butter mixture under the skin and towards the front of the bird, evenly spreading it over the breast. Work the rest of the butter mixture under the skin of the legs. It's okay if it's coming out the side; it will drip onto the potatoes as it cooks. Season the interior and exterior of the chicken liberally with the remaining celery salt mixture and some salt and pepper.
Put the potatoes and shallots in a large skillet. Drizzle with the olive oil and season with salt and pepper. Put the skillet on the center of the grill. Arrange 2 bricks on either side of the skillet. Set a cooling rack on top of the bricks over the skillet. Put the chicken on the rack and reduce the heat to low. The grill should maintain a temperature of 325 degrees F.
Roast the chicken for approximately 30 minutes. If the potatoes begin to brown too much, turn them and add a splash of water to deglaze the bottom. After 30 minutes, add the zucchini and yellow squash to the skillet. Cook until the chicken reaches an internal temperature of 155 degrees F, another 20 to 30 minutes.
Transfer the chicken to a cutting board to rest for 5 minutes before carving. Top the potato-squash mixture with the basil, jalapeño slices, the juice of the remaining lemon half and some salt. Toss to combine. Carve the chicken and serve with potato-squash mixture on the side.