In a 3-quart saucepan, boil apple cider over high heat until reduced to 1/3 cup of cider syrup, 30-40 minutes. (Pour syrup into a heatproof measuring cup to check on the reduction amount during the last 5-10 minutes of cooking.) Remove from heat.
Meanwhile, lightly coat an 8-x-8-inch straight-sided metal baking pan with cooking spray. (The spray will help keep the parchment paper securely in place.) Cut two 8-x-11-inch pieces parchment paper. Line the bottom and sides of pan with paper, leaving 2-inches of overhang on all sides. Spray paper with cooking spray.
Add butter, brown sugar, honey and goat milk into the hot cider syrup; stir until butter is melted. Return pot to just above medium heat with a candy thermometer attached to the side. Cook, undisturbed, until the thermometer reads 250° or hard ball stage, 8-12 minutes, watching closely. Immediately remove from heat and use the candy thermometer to stir in salt.
Pour caramel into the prepared pan. Let cool, uncovered, at room temperature for 2 hours, then sprinkle with flaky salt. Cover and refrigerate at least 1 hour or overnight.
Use the parchment paper overhang to transfer caramel to a cutting board. If refrigerated overnight, let sit at room temperature for about 20 minutes before slicing. Use a large knife to cut the caramel into bite-sized squares or rectangles. Wrap each caramel in waxed paper, twisting the sides to seal. Store in an airtight container at room temperature for up to two weeks.