Line 8”x8” baking pan with parchment paper, so that paper covers bottom of pan and comes up sides to hang at least 2” over edges. Set aside.
In small saucepan over medium-high heat, bring butter, coconut milk and salt to boil, stirring until butter melts. Remove pot from heat. Cover and keep warm.
Meanwhile, in medium, heavy saucepan over medium-high heat, bring sugar, corn syrup and ½ cup water to boil, stirring until sugar dissolves. Using wet pastry brush, wipe off any sugar that sticks to sides of pan. Cook, without stirring, swirling pan for even heating, until syrup turns amber and temperature registers 298°F on candy thermometer, 10-12 minutes. Remove pot from heat.
Slowly and carefully pour coconut milk mixture into pot with hot caramel (use caution, milk and sugar mixture will bubble and splatter). Stir to combine. Return pot to stove over medium-high heat. Bring coconut-caramel mixture to boil, stirring with wooden spoon or heat-resistant spatula and taking care to scrape bottom of pot, until coconut-caramel mixture reaches 248°F on candy thermometer, 22-25 minutes.
Carefully pour hot coconut-caramel mixture into prepared pan. Let sit a few seconds. Sprinkle flaked coconut over top of caramel. Let sit until caramel is just warm. Transfer pan to refrigerator. Chill until cold, about 2 hours or overnight. To remove caramel from pan, lift up on parchment paper handles and transfer to cutting board. Peel back on parchment paper to remove and discard. Cut caramel into ¾”x1” rectangles. Wrap in parchment paper, or place into mini cupcake liners, if desired.