Butter a half-sheet pan, line with a silicone baking sheet, and lightly grease with butter. Set aside.
Combine the sugar, cocoa powder, and salt in a 4-quart saucepan. Whisk until thoroughly combined. Add the corn syrup, water, and vinegar to the pan and place over high heat. Stir with a wooden spoon or heatproof spatula until the sugar and cocoa are well combined. Cook until the mixture reaches 250ºF on a digital instant-read thermometer.
Remove the pan from the heat, add the butter, and stir. Carefully pour the mixture into the prepared pan and set aside for 10 minutes. Using the silicone mat as a holding device, fold the taffy back on itself over and over until it is cool enough to hold in your hands.
Once you are able to handle the taffy, don vinyl gloves, butter them, pick up the taffy, and begin to pull, folding the taffy back on itself repeatedly and twisting as you go. Taffy is done when it lightens in color, takes on a sheen, and becomes hard to pull, 5 to 10 minutes. Divide taffy into fourths. Roll each fourth into a 1-inch wide log, and cut into 1/2-inch pieces. Make sure to keep pieces separated or they will stick to each other. Wrap individual pieces of candy in waxed paper. Store in airtight container for up to 5 days.