You want them to be free of pesticides and other contaminants.
Simply dunk the flowers in a bowl of clean water, swish them around, then pat dry. This should remove any debris and teeny tiny bugs that take up residence between the florets.
If you want dainty wisps to sprinkle over your food, gently pull the florets away from the center of the flower head with your fingers.
It’s best to store them whole, and I find it easiest to seal them inside a plastic bag or lidded container. They should keep for up to one week in the fridge.
If you don’t grow chives at home, you can usually find chive blossoms in specialty grocers and farmers’ markets in May and June. They’re hard to find after that as their season is short, so be sure to grab them if you see them.