Use charcoal briquets instead of wood to more precisely control the fire's heat.
Combine flour, sugar, dried buttermilk, cocoa, baking soda, salt, and 1/2 cup chocolate chips in a lidded container or a resealable plastic bag. Pour 1/3 cup oil and the vanilla into a second container with a snug lid. Cut a circle of parchment paper to fit the bottom of a 4-qt. camp dutch oven.
Fill a charcoal chimney starter one-third with briquets, set in a firepit, ignite, and let burn until briquets are spotted gray, about 20 minutes.
Meanwhile, generously oil dutch oven, line with parchment paper circle, and oil paper. Pour flour mixture into a medium bowl.
When fire is ready, add oil mixture and 1 cup water to flour mixture and stir until blended. Scrape into dutch oven and sprinkle with remaining 1/2 cup chocolate chips.
Using tongs, space 8 coals in firepit in a circle a little smaller than the dutch oven. Set dutch oven on coals, checking that it's level. Set lid on top, then arrange 14 coals on lid around the lip and 2 coals in center of lid. Set any extra coals aside.
Bake cake until a skewer inserted into center comes out clean, 25 to 30 minutes; to check, lift lid by sliding tongs through lid's center handle and bracing them against side of lid closest to you, then tilting lid up. Remove lid and let cake cool at least 15 minutes before cutting into wedges.
*Find at well-stocked grocery stores.
Make ahead: Through step 1, up to 3 months, mix chilled and oil stored airtight.