In the bowl of a large food processor fitted with an s-blade, process the dates until a sticky ball is formed. Add in the flax, oats, peanut butter, salt, and vanilla and process again until finely ground and crumbly. The mixture should stick together easily when pressed between your fingers. If the mixture doesn't stick together, try adding one tablespoon of water and process again.
Use your hands to roll the dough into bite-sized balls, about 1 to 1 1/2 inches in diameter. Arrange them in a single layer on a plate or baking sheet, cover tightly, and store in the fridge or freezer until ready to serve. (Once cold, you can pile them into a smaller storage container without them sticking to each other.)