Drain pickles and discard the liquid. Place the pickles in a medium size bowl.
Peel onion and cut in half vertically. Lay cut side down and cut vertically into 1/4-inch slices to create slivers and add to pickles in the bowl. Add sugars, vinegar, garlic, pepper flakes, mustard seeds, and turmeric to the bowl; stir well.
Cover and refrigerate overnight so the pickles will have a kick to them from the crushed red pepper. Stir at least once. Keep them in the bowl during this time because they won’t fit back in the jar yet. The sugars will dissolve overnight and the onions will "shrink".
Spoon pickles back into the same pickle jar with a slotted spoon if they will fit) or in a decorative 4 to 5-cup canning jar with a lid . The onions will have reduced in volume enough after 24 hours to fit in the jar. Pour the liquid over the pickles and onions. Keep them refrigerated for up to 3 weeks.