Preheat a grill.
Combine flour, oatmeal, sugar, and butter in a large bowl; mix until well combined. Place 3/4 of mixture along the bottom of a Dutch oven. Spread fruit over top, then sprinkle with the rest of the oatmeal mixture. Place on rack of hot grill; 1/3 of the charcoal must be on top and 2/3 of the charcoal must be on the bottom. The key to cooking it is not to open the Dutch oven until you have smelled the cobbler for 10 minutes. Every time you open the Dutch oven you lose the heat. Serve warm.