Preheat the grill to 450°F.
Generously sprinkle a work surface with all-purpose flour. Stretch/roll the pizza dough into a 12-inch circle. Transfer to a pizza peel, cutting board or rimless baking sheet that is generously sprinkled with semolina flour or corn meal.
Grease the grill grate.
Carefully slide the shaped dough onto the preheated grill. Grill for 4-5 minutes over indirect heat until the bottom is golden brown and top is puffy with air bubbles. Transfer the crust to the pizza peel. Brush the top of the crust with olive oil then flip it over so the grilled side is up.
Spread BBQ sauce over the grilled side of the dough. Sprinkle with shredded cheese. Top with chicken, red onion, and cherry tomatoes. Return to the grill over indirect heat. Grill until the crust is golden brown and cheese is melted, about 5-10 minutes.
While the pizza cooks, make the hot honey butter. Heat together the butter, honey, hot sauce, salt and red pepper flakes in a small saucepan over medium heat, stirring often until heated through.
Remove the pizza from the grill and drizzle with lots of hot honey butter. Slice and enjoy!