Peel radish and carrot, removing the ends.
Using the mandolin, slice the radish and carrots into thin long strings.
Place the radish and carrots into the mixing bowl and cover with cold water. Let sit for at least a half hour. This is important, as the daikon radish has a pungent odor when pickled and this step helps reduce it. After the wait, rinse the vegetables and place them into the container.
Mix the water, vinegar, sugar and pepper flakes in the sauce pan, heat until boiling and the sugar has disolved.
Pour the liquid over the vegetables, topping up with water if necessary to ensure that they are completely covered.
Seal the container, let it cool on the counter and then refrigerate.
The pickles are best the day after being made.