Prepare the Swiss Chard Stems: Wash the rainbow Swiss chard stems thoroughly, then cut them into 2-3 inch pieces. Set aside.
Make the Pickling Brine: In a medium saucepan, combine the water, pickling vinegar, sugar, and kosher salt. Stir the mixture over medium heat until the sugar and salt are fully dissolved. Remove the pan from heat and allow the brine to cool slightly.
Prepare the Jars: In a clean, heatproof jar, add the garlic cloves, 1/4 teaspoon of black peppercorns, yellow mustard seed, celery seed, red pepper flakes, and fresh dill sprigs.
Pack the Jars: Place the cut Swiss chard stems into the jar, packing them tightly but leaving about 1/2 inch of space at the top.
Add the Brine: Pour the slightly cooled pickling brine over the Swiss chard stems, making sure they are completely submerged. If necessary, press the stems down with a spoon to release any air bubbles.
Seal the Jar: Add the remaining black peppercorns on top, then seal the jar with a tight-fitting lid.
Pickling Process: Allow the jar to cool to room temperature, then refrigerate. The pickled Swiss chard stems will be ready to eat after 24 hours, but for best flavor, let them pickle for at least 3 days.