Combine the rice-wine vinegar, mirin, sugar, and salt in a small bowl.
Bring a pot of water to a boil; cook rice noodles until tender, about 3 minutes. Drain in a colander; transfer to a bowl.
Pour 2 tablespoons rice-wine-vinegar mixture over noodles, and set aside. Place the cucumber and jicama in a bowl, and combine with 2 tablespoons rice-wine-vinegar mixture.
Fill a medium bowl with warm water, and dip rice-paper wrappers, a few at a time, until malleable. Lay wrapper on a clean towel, and arrange small bundle of rice noodles, 4 pieces cucumber, 2 pieces jicama, several mint leaves, and 1 chive across lower quarter of wrapper. Roll, folding in ends as you go, forming a tight roll. Place on a plate lined with damp paper towels, and repeat until all 24 rolls are formed. Keep covered with damp paper towels until ready to serve.
For the dipping sauce, add fish sauce, chile pepper and carrot to remaining reserved rice-wine-vinegar mixture. Just before serving, cut rolls in half on the diagonal, and arrange on a serving plate with dipping sauce.