Place 1½ cups figs and 1 cup dates in a medium heatproof bowl; cover with hot water. Let stand at room temperature until slightly softened, 20 to 30 minutes.
Line a baking sheet with parchment paper. Drain figs and dates; transfer to a food processor. Pulse until coarsely chopped, about 5 pulses. Add 1½ cups oats, 3 tablespoons almond butter, 2 tablespoons flaxseed, 1 tablespoon each orange juice and vanilla and ¾ teaspoon each cinnamon and salt; pulse until well combined, about 25 pulses, stopping to scrape down sides of bowl as needed. Using a cookie scoop or your hands, scoop the mixture into about 1½-tablespoon portions; roll with your hands into smooth balls.
Place the balls on the prepared baking sheet. Cover and refrigerate until chilled, at least 1 hour.
