Combine soy milk, yeast, and sugar in a bowl. Let sit until foamy, about 15 minutes. Add vinegar and oil.
Stir rice flour, tapioca starch, xanthan gum, gelatin, and herbes de Provence together in a bowl. Transfer to the bowl of a stand mixer with a paddle attachment. Add the yeast mixture; mix on medium to high speed until dough is sticky and well combined, about 6 minutes.
Preheat oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper and spray with cooking spray.
Place dough in a resealable plastic bag and cut a 1/2- to 3/4-inch triangle from one of the bottom corners. Squeeze dough onto the prepared baking sheet in long strips to create 10 breadsticks.
Bake in the preheated oven until golden brown, 10 to 12 minutes.