In heavy medium saucepan, combine sugar, cocoa powder, and salt. Stir until thoroughly combined. Add corn syrup, water, and vinegar to pan and place over medium heat. Stir until sugar and cocoa dissolve, raise heat to high and bring to a boil. Turn heat down to low, clip candy thermometer to side of pan and cook until mixture reaches 260 degrees F. Remove pan from heat, add the butter and stir. Butter edges of sheet pan, line with silicone baking sheet and pour on taffy. Allow to cool until you are able to handle it.
Once you are able to handle the taffy, don vinyl gloves, butter them, and begin to fold taffy in thirds using the silicone mat. Pick up taffy and begin to pull folding the taffy back on itself repeatedly twisting as you go. Taffy is done when it lightens in color, takes on a sheen, and becomes too hard to pull. Roll into log, cut into fourths, roll each fourth into a 1-inch wide log, and cut into 1-inch pieces. Making sure to keep pieces separated or they will stick to each other. Wrap individual pieces of candy in waxed paper. Store in airtight container 3 to 5 days.