In a large serving bowl, combine the carrots, broccoli slaw, jalapeno and red onion. Set aside.
In a small saucepan, add the vinegar, lime zest, lime juice, salt, sugar, red pepper flakes and the black pepper. Bring to a light boil over low heat. Remove from heat and allow to cool for a few minutes.
Add the olive oil to the vinegar mixture, pour over the vegetables and toss together to combine. Refrigerate until serving.